Chapter 3: Factors, Multiples, Primes, and Divisibility
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Factors, Multiples, Primes, and Divisibility with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Factor (a number that divides another number exactly)
- Multiple (a result of multiplying a number by a whole number)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
3.1 Factors
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Factors. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.2 Factor pairs
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Factor pairs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.3 Multiples
A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples .
Answer: 18, 36, 54, 72, 90
Worked Example 2
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples .
Answer: 24, 48, 72, 96, 120
Worked Example 3
Problem: List the first five positive multiples of 36.
- Multiply 36 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples .
Answer: 36, 72, 108, 144, 180
Worked Example 4
Problem: List the first five positive multiples of 45.
- Multiply 45 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples .
Answer: 45, 90, 135, 180, 225
Worked Example 5
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples .
Answer: 60, 120, 180, 240, 300
Worked Example 6
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 18, 36, 54, 72, 90
Worked Example 7
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 24, 48, 72, 96, 120
Worked Example 8
Problem: List the first five positive multiples of 30.
- Multiply 30 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 30, 60, 90, 120, 150
Worked Example 9
Problem: List the first five positive multiples of 42.
- Multiply 42 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 42, 84, 126, 168, 210
Worked Example 10
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 60, 120, 180, 240, 300
Practice Exercise
Create one new question about Multiples. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.4 Common factors
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Common factors. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.5 Greatest common factor
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Greatest common factor. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.6 Common multiples
A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples .
Answer: 18, 36, 54, 72, 90
Worked Example 2
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples .
Answer: 24, 48, 72, 96, 120
Worked Example 3
Problem: List the first five positive multiples of 36.
- Multiply 36 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples .
Answer: 36, 72, 108, 144, 180
Worked Example 4
Problem: List the first five positive multiples of 45.
- Multiply 45 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples .
Answer: 45, 90, 135, 180, 225
Worked Example 5
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples .
Answer: 60, 120, 180, 240, 300
Worked Example 6
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 18, 36, 54, 72, 90
Worked Example 7
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 24, 48, 72, 96, 120
Worked Example 8
Problem: List the first five positive multiples of 30.
- Multiply 30 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 30, 60, 90, 120, 150
Worked Example 9
Problem: List the first five positive multiples of 42.
- Multiply 42 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 42, 84, 126, 168, 210
Worked Example 10
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 60, 120, 180, 240, 300
Practice Exercise
Create one new question about Common multiples. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.7 Least common multiple
A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple .
Answer: 18, 36, 54, 72, 90
Worked Example 2
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple .
Answer: 24, 48, 72, 96, 120
Worked Example 3
Problem: List the first five positive multiples of 36.
- Multiply 36 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple .
Answer: 36, 72, 108, 144, 180
Worked Example 4
Problem: List the first five positive multiples of 45.
- Multiply 45 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple .
Answer: 45, 90, 135, 180, 225
Worked Example 5
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple .
Answer: 60, 120, 180, 240, 300
Worked Example 6
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 18, 36, 54, 72, 90
Worked Example 7
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 24, 48, 72, 96, 120
Worked Example 8
Problem: List the first five positive multiples of 30.
- Multiply 30 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 30, 60, 90, 120, 150
Worked Example 9
Problem: List the first five positive multiples of 42.
- Multiply 42 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 42, 84, 126, 168, 210
Worked Example 10
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples are produced by multiplying the number by whole numbers.
Answer: 60, 120, 180, 240, 300
Practice Exercise
Create one new question about Least common multiple. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.8 Prime numbers
A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Is 18 prime or composite?
- Factors are 1, 2, 3, 6, 9, 18.
- A prime has exactly two positive factors.
Very beginner explanation: A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers .
Answer: Composite
Worked Example 2
Problem: Is 24 prime or composite?
- Factors are 1, 2, 3, 4, 6, 8, 12, 24.
- A prime has exactly two positive factors.
Very beginner explanation: A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers .
Answer: Composite
Worked Example 3
Problem: Is 36 prime or composite?
- Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
- A prime has exactly two positive factors.
Very beginner explanation: A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers .
Answer: Composite
Worked Example 4
Problem: Is 45 prime or composite?
- Factors are 1, 3, 5, 9, 15, 45.
- A prime has exactly two positive factors.
Very beginner explanation: A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers .
Answer: Composite
Worked Example 5
Problem: Is 60 prime or composite?
- Factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- A prime has exactly two positive factors.
Very beginner explanation: A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers .
Answer: Composite
Worked Example 6
Problem: Is 18 prime or composite?
- List its factors: 1, 2, 3, 6, 9, 18.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 7
Problem: Is 24 prime or composite?
- List its factors: 1, 2, 3, 4, 6, 8, 12, 24.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 8
Problem: Is 30 prime or composite?
- List its factors: 1, 2, 3, 5, 6, 10, 15, 30.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 9
Problem: Is 42 prime or composite?
- List its factors: 1, 2, 3, 6, 7, 14, 21, 42.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 10
Problem: Is 60 prime or composite?
- List its factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Practice Exercise
Create one new question about Prime numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.9 Composite numbers
Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: Is 18 prime or composite?
- List its factors: 1, 2, 3, 6, 9, 18.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 7
Problem: Is 24 prime or composite?
- List its factors: 1, 2, 3, 4, 6, 8, 12, 24.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 8
Problem: Is 30 prime or composite?
- List its factors: 1, 2, 3, 5, 6, 10, 15, 30.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 9
Problem: Is 42 prime or composite?
- List its factors: 1, 2, 3, 6, 7, 14, 21, 42.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 10
Problem: Is 60 prime or composite?
- List its factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Practice Exercise
Create one new question about Composite numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.10 Prime factorization
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Is 18 prime or composite?
- Factors are 1, 2, 3, 6, 9, 18.
- A prime has exactly two positive factors.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization .
Answer: Composite
Worked Example 2
Problem: Is 24 prime or composite?
- Factors are 1, 2, 3, 4, 6, 8, 12, 24.
- A prime has exactly two positive factors.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization .
Answer: Composite
Worked Example 3
Problem: Is 36 prime or composite?
- Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
- A prime has exactly two positive factors.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization .
Answer: Composite
Worked Example 4
Problem: Is 45 prime or composite?
- Factors are 1, 3, 5, 9, 15, 45.
- A prime has exactly two positive factors.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization .
Answer: Composite
Worked Example 5
Problem: Is 60 prime or composite?
- Factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- A prime has exactly two positive factors.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization .
Answer: Composite
Worked Example 6
Problem: Is 18 prime or composite?
- List its factors: 1, 2, 3, 6, 9, 18.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 7
Problem: Is 24 prime or composite?
- List its factors: 1, 2, 3, 4, 6, 8, 12, 24.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 8
Problem: Is 30 prime or composite?
- List its factors: 1, 2, 3, 5, 6, 10, 15, 30.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 9
Problem: Is 42 prime or composite?
- List its factors: 1, 2, 3, 6, 7, 14, 21, 42.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Worked Example 10
Problem: Is 60 prime or composite?
- List its factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- A prime number has exactly two positive factors.
Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.
Answer: Composite
Practice Exercise
Create one new question about Prime factorization. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.11 Factor trees
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Factor trees. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.12 Divisibility rules
Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Test whether 18 is divisible by 3.
- Add its digits: 9.
- If the digit sum is divisible by 3, the number is divisible by 3.
Very beginner explanation: Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Yes
Worked Example 2
Problem: Test whether 24 is divisible by 3.
- Add its digits: 6.
- If the digit sum is divisible by 3, the number is divisible by 3.
Very beginner explanation: Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Yes
Worked Example 3
Problem: Test whether 36 is divisible by 3.
- Add its digits: 9.
- If the digit sum is divisible by 3, the number is divisible by 3.
Very beginner explanation: Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Yes
Worked Example 4
Problem: Test whether 45 is divisible by 3.
- Add its digits: 9.
- If the digit sum is divisible by 3, the number is divisible by 3.
Very beginner explanation: Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Yes
Worked Example 5
Problem: Test whether 60 is divisible by 3.
- Add its digits: 6.
- If the digit sum is divisible by 3, the number is divisible by 3.
Very beginner explanation: Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Yes
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Divisibility rules. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.13 Grouping applications
Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: Explain Grouping applications in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Grouping applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Grouping applications and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Grouping applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Grouping applications using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Grouping applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Grouping applications problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Grouping applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Grouping applications could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Grouping applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Grouping applications. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.14 Repeating-schedule applications
Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 18.
- Multiply 18 by 1, 2, 3, 4, and 5.
Very beginner explanation: Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 18, 36, 54, 72, 90
Worked Example 2
Problem: List the first five positive multiples of 24.
- Multiply 24 by 1, 2, 3, 4, and 5.
Very beginner explanation: Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 24, 48, 72, 96, 120
Worked Example 3
Problem: List the first five positive multiples of 36.
- Multiply 36 by 1, 2, 3, 4, and 5.
Very beginner explanation: Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 36, 72, 108, 144, 180
Worked Example 4
Problem: List the first five positive multiples of 45.
- Multiply 45 by 1, 2, 3, 4, and 5.
Very beginner explanation: Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 45, 90, 135, 180, 225
Worked Example 5
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 60, 120, 180, 240, 300
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Repeating-schedule applications. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Factors . Show your reasoning and check your answer.
- Create and solve a new question about Factor pairs . Show your reasoning and check your answer.
- Create and solve a new question about Multiples . Show your reasoning and check your answer.
- Create and solve a new question about Common factors . Show your reasoning and check your answer.
- Create and solve a new question about Greatest common factor . Show your reasoning and check your answer.
- Create and solve a new question about Common multiples . Show your reasoning and check your answer.
- Create and solve a new question about Least common multiple . Show your reasoning and check your answer.
- Create and solve a new question about Prime numbers . Show your reasoning and check your answer.
- Create and solve a new question about Composite numbers . Show your reasoning and check your answer.
- Create and solve a new question about Prime factorization . Show your reasoning and check your answer.
- Create and solve a new question about Factor trees . Show your reasoning and check your answer.
- Create and solve a new question about Divisibility rules . Show your reasoning and check your answer.
Common Mistakes
- Ignoring place value or signs.
- Using an operation before checking what the question asks.
- Skipping estimation and accepting an unreasonable result.
- Forgetting the correct order of operations.
30 Review Questions and Answers
Q1. What is important to remember about Factors?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factors.
Q2. What is important to remember about Factor pairs?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor pairs.
Q3. What is important to remember about Multiples?
Answer: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Multiples.
Q4. What is important to remember about Common factors?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Common factors.
Q5. What is important to remember about Greatest common factor?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Greatest common factor.
Q6. What is important to remember about Common multiples?
Answer: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Common multiples.
Q7. What is important to remember about Least common multiple?
Answer: A multiple (a result of multiplying a number by a whole number) is useful for common denominators and repeating schedules. This topic focuses on Least common multiple.
Q8. What is important to remember about Prime numbers?
Answer: A prime number (a whole number greater than 1 with exactly two positive factors) can be used to build prime factorizations. This topic focuses on Prime numbers.
Q9. What is important to remember about Composite numbers?
Answer: Composite numbers is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Prime factorization?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Prime factorization.
Q11. What is important to remember about Factor trees?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factor trees.
Q12. What is important to remember about Divisibility rules?
Answer: Divisibility rules is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Grouping applications?
Answer: Grouping applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. What is important to remember about Repeating-schedule applications?
Answer: Repeating-schedule applications is an important Grade 7 idea in Factors, Multiples, Primes, and Divisibility. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q15. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q16. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q17. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q18. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q19. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q20. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q21. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q22. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q23. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q24. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q25. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q26. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q27. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q28. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q29. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q30. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.