Chapter 9: Factors, Multiples, Prime, and Composite Numbers
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Factors, Multiples, Prime, and Composite Numbers in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Factors (A factor is a whole number that divides another whole number exactly.)
- Multiples (A multiple is a result found by multiplying a number by a whole number.)
- Prime numbers (A prime number has exactly two positive factors: 1 and itself.)
- Composite numbers (A composite number has more than two positive factors.)
- Grouping and schedule applications (Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
9.1 Factors
A factor is a whole number that divides another whole number exactly. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List all positive factors of 48.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Worked Example 2
Problem: List all positive factors of 86.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 43, 86
Worked Example 3
Problem: List all positive factors of 79.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 79
Worked Example 4
Problem: List all positive factors of 60.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 5
Problem: List all positive factors of 36.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 6
Problem: List all positive factors of 61.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 61
Worked Example 7
Problem: List all positive factors of 62.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 31, 62
Worked Example 8
Problem: List all positive factors of 33.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 11, 33
Worked Example 9
Problem: List all positive factors of 63.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 7, 9, 21, 63
Worked Example 10
Problem: List all positive factors of 31.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 31
Practice Exercise
Create one new Grade 6 problem about Factors. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.2 Factor pairs
A factor is a whole number that divides another whole number exactly. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List all positive factors of 55.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 5, 11, 55
Worked Example 2
Problem: List all positive factors of 15.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 5, 15
Worked Example 3
Problem: List all positive factors of 71.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 71
Worked Example 4
Problem: List all positive factors of 75.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 5, 15, 25, 75
Worked Example 5
Problem: List all positive factors of 47.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 47
Worked Example 6
Problem: List all positive factors of 58.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 29, 58
Worked Example 7
Problem: List all positive factors of 36.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 8
Problem: List all positive factors of 34.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 17, 34
Worked Example 9
Problem: List all positive factors of 89.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 89
Worked Example 10
Problem: List all positive factors of 57.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 19, 57
Practice Exercise
Create one new Grade 6 problem about Factor pairs. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.3 Multiples
A multiple is a result found by multiplying a number by a whole number. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 22.
- Multiply 22 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 22, 44, 66, 88, 110
Worked Example 2
Problem: List the first five positive multiples of 61.
- Multiply 61 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 61, 122, 183, 244, 305
Worked Example 3
Problem: List the first five positive multiples of 25.
- Multiply 25 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 25, 50, 75, 100, 125
Worked Example 4
Problem: List the first five positive multiples of 19.
- Multiply 19 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 19, 38, 57, 76, 95
Worked Example 5
Problem: List the first five positive multiples of 46.
- Multiply 46 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 46, 92, 138, 184, 230
Worked Example 6
Problem: List the first five positive multiples of 37.
- Multiply 37 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 37, 74, 111, 148, 185
Worked Example 7
Problem: List the first five positive multiples of 59.
- Multiply 59 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 59, 118, 177, 236, 295
Worked Example 8
Problem: List the first five positive multiples of 21.
- Multiply 21 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 21, 42, 63, 84, 105
Worked Example 9
Problem: List the first five positive multiples of 71.
- Multiply 71 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 71, 142, 213, 284, 355
Worked Example 10
Problem: List the first five positive multiples of 45.
- Multiply 45 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 45, 90, 135, 180, 225
Practice Exercise
Create one new Grade 6 problem about Multiples. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.4 Common factors
A factor is a whole number that divides another whole number exactly. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List all positive factors of 23.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 23
Worked Example 2
Problem: List all positive factors of 12.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 12
Worked Example 3
Problem: List all positive factors of 13.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 13
Worked Example 4
Problem: List all positive factors of 76.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 4, 19, 38, 76
Worked Example 5
Problem: List all positive factors of 17.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 17
Worked Example 6
Problem: List all positive factors of 84.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Worked Example 7
Problem: List all positive factors of 59.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 59
Worked Example 8
Problem: List all positive factors of 50.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 5, 10, 25, 50
Worked Example 9
Problem: List all positive factors of 25.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 5, 25
Worked Example 10
Problem: List all positive factors of 33.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 11, 33
Practice Exercise
Create one new Grade 6 problem about Common factors. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.5 Greatest common factor introduction
A factor is a whole number that divides another whole number exactly. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List all positive factors of 84.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Worked Example 2
Problem: List all positive factors of 15.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 3, 5, 15
Worked Example 3
Problem: List all positive factors of 54.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 6, 9, 18, 27, 54
Worked Example 4
Problem: List all positive factors of 88.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 4, 8, 11, 22, 44, 88
Worked Example 5
Problem: List all positive factors of 29.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 29
Worked Example 6
Problem: List all positive factors of 88.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 4, 8, 11, 22, 44, 88
Worked Example 7
Problem: List all positive factors of 30.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 8
Problem: List all positive factors of 32.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 4, 8, 16, 32
Worked Example 9
Problem: List all positive factors of 82.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 41, 82
Worked Example 10
Problem: List all positive factors of 48.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Practice Exercise
Create one new Grade 6 problem about Greatest common factor introduction. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.6 Common multiples
A multiple is a result found by multiplying a number by a whole number. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 46.
- Multiply 46 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 46, 92, 138, 184, 230
Worked Example 2
Problem: List the first five positive multiples of 84.
- Multiply 84 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 84, 168, 252, 336, 420
Worked Example 3
Problem: List the first five positive multiples of 41.
- Multiply 41 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 41, 82, 123, 164, 205
Worked Example 4
Problem: List the first five positive multiples of 60.
- Multiply 60 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 60, 120, 180, 240, 300
Worked Example 5
Problem: List the first five positive multiples of 45.
- Multiply 45 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 45, 90, 135, 180, 225
Worked Example 6
Problem: List the first five positive multiples of 13.
- Multiply 13 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 13, 26, 39, 52, 65
Worked Example 7
Problem: List the first five positive multiples of 83.
- Multiply 83 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 83, 166, 249, 332, 415
Worked Example 8
Problem: List the first five positive multiples of 48.
- Multiply 48 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 48, 96, 144, 192, 240
Worked Example 9
Problem: List the first five positive multiples of 34.
- Multiply 34 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 34, 68, 102, 136, 170
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 come from repeated multiplication by whole numbers.
Answer: 60, 120, 180, 240, 300
Practice Exercise
Create one new Grade 6 problem about Common multiples. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.7 Least common multiple introduction
A multiple is a result found by multiplying a number by a whole number. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the first five positive multiples of 61.
- Multiply 61 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 61, 122, 183, 244, 305
Worked Example 2
Problem: List the first five positive multiples of 16.
- Multiply 16 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 16, 32, 48, 64, 80
Worked Example 3
Problem: List the first five positive multiples of 69.
- Multiply 69 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 69, 138, 207, 276, 345
Worked Example 4
Problem: List the first five positive multiples of 69.
- Multiply 69 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 69, 138, 207, 276, 345
Worked Example 5
Problem: List the first five positive multiples of 61.
- Multiply 61 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 61, 122, 183, 244, 305
Worked Example 6
Problem: List the first five positive multiples of 72.
- Multiply 72 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 72, 144, 216, 288, 360
Worked Example 7
Problem: List the first five positive multiples of 84.
- Multiply 84 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 84, 168, 252, 336, 420
Worked Example 8
Problem: List the first five positive multiples of 79.
- Multiply 79 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 79, 158, 237, 316, 395
Worked Example 9
Problem: List the first five positive multiples of 22.
- Multiply 22 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 22, 44, 66, 88, 110
Worked Example 10
Problem: List the first five positive multiples of 75.
- Multiply 75 by 1, 2, 3, 4, and 5.
Very beginner explanation: Multiples come from repeated multiplication by whole numbers.
Answer: 75, 150, 225, 300, 375
Practice Exercise
Create one new Grade 6 problem about Least common multiple introduction. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.8 Prime numbers
A prime number has exactly two positive factors: 1 and itself. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Is 52 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 13, 26, 52.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 2
Problem: Is 51 prime or composite?
- List or test its positive factors.
- Factors: 1, 3, 17, 51.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 3
Problem: Is 68 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 17, 34, 68.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 4
Problem: Is 42 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 6, 7, 14, 21, 42.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 5
Problem: Is 64 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 8, 16, 32, 64.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 6
Problem: Is 57 prime or composite?
- List or test its positive factors.
- Factors: 1, 3, 19, 57.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 7
Problem: Is 44 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 11, 22, 44.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 8
Problem: Is 58 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 29, 58.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 9
Problem: Is 39 prime or composite?
- List or test its positive factors.
- Factors: 1, 3, 13, 39.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 10
Problem: Is 77 prime or composite?
- List or test its positive factors.
- Factors: 1, 7, 11, 77.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Practice Exercise
Create one new Grade 6 problem about Prime numbers. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.9 Composite numbers
A composite number has more than two positive factors. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Is 60 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20....
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 2
Problem: Is 84 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28....
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 3
Problem: Is 80 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 4
Problem: Is 70 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 5, 7, 10, 14, 35, 70.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 5
Problem: Is 82 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 41, 82.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 6
Problem: Is 86 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 43, 86.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 7
Problem: Is 72 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24....
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 8
Problem: Is 25 prime or composite?
- List or test its positive factors.
- Factors: 1, 5, 25.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 9
Problem: Is 32 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 8, 16, 32.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 10
Problem: Is 51 prime or composite?
- List or test its positive factors.
- Factors: 1, 3, 17, 51.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Practice Exercise
Create one new Grade 6 problem about Composite numbers. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.10 Prime factorization introduction
A factor is a whole number that divides another whole number exactly. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Is 59 prime or composite?
- List or test its positive factors.
- Factors: 1, 59.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Prime
Worked Example 2
Problem: Is 29 prime or composite?
- List or test its positive factors.
- Factors: 1, 29.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Prime
Worked Example 3
Problem: Is 66 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 6, 11, 22, 33, 66.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 4
Problem: Is 18 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 6, 9, 18.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 5
Problem: Is 54 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 3, 6, 9, 18, 27, 54.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 6
Problem: Is 87 prime or composite?
- List or test its positive factors.
- Factors: 1, 3, 29, 87.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 7
Problem: Is 13 prime or composite?
- List or test its positive factors.
- Factors: 1, 13.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Prime
Worked Example 8
Problem: Is 67 prime or composite?
- List or test its positive factors.
- Factors: 1, 67.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Prime
Worked Example 9
Problem: Is 51 prime or composite?
- List or test its positive factors.
- Factors: 1, 3, 17, 51.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Worked Example 10
Problem: Is 80 prime or composite?
- List or test its positive factors.
- Factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.
Answer: Composite
Practice Exercise
Create one new Grade 6 problem about Prime factorization introduction. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.11 Factor trees
A factor is a whole number that divides another whole number exactly. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List all positive factors of 23.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 23
Worked Example 2
Problem: List all positive factors of 68.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 4, 17, 34, 68
Worked Example 3
Problem: List all positive factors of 68.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 4, 17, 34, 68
Worked Example 4
Problem: List all positive factors of 31.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 31
Worked Example 5
Problem: List all positive factors of 13.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 13
Worked Example 6
Problem: List all positive factors of 19.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 19
Worked Example 7
Problem: List all positive factors of 37.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 37
Worked Example 8
Problem: List all positive factors of 65.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 5, 13, 65
Worked Example 9
Problem: List all positive factors of 84.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Worked Example 10
Problem: List all positive factors of 19.
- Test whole numbers that divide exactly.
- Pair factors when their product equals the number.
Very beginner explanation: Factors divide a number with no remainder.
Answer: 1, 19
Practice Exercise
Create one new Grade 6 problem about Factor trees. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
9.12 Grouping and schedule applications
Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Use Grouping and schedule applications to analyze the values 3 and 13. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 2
Problem: Use Grouping and schedule applications to analyze the values 24 and 11. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 3
Problem: Use Grouping and schedule applications to analyze the values 6 and 6. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 4
Problem: Use Grouping and schedule applications to analyze the values 30 and 6. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 5
Problem: Use Grouping and schedule applications to analyze the values 28 and 20. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 6
Problem: Use Grouping and schedule applications to analyze the values 25 and 8. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 7
Problem: Use Grouping and schedule applications to analyze the values 24 and 4. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 8
Problem: Use Grouping and schedule applications to analyze the values 20 and 15. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 9
Problem: Use Grouping and schedule applications to analyze the values 25 and 18. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 10
Problem: Use Grouping and schedule applications to analyze the values 2 and 10. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Practice Exercise
Create one new Grade 6 problem about Grouping and schedule applications. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
30 Review Questions and Answers
Q1. What is important to understand about Factors?
Answer: A factor is a whole number that divides another whole number exactly.
Q2. What is important to understand about Factor pairs?
Answer: A factor is a whole number that divides another whole number exactly.
Q3. What is important to understand about Multiples?
Answer: A multiple is a result found by multiplying a number by a whole number.
Q4. What is important to understand about Common factors?
Answer: A factor is a whole number that divides another whole number exactly.
Q5. What is important to understand about Greatest common factor introduction?
Answer: A factor is a whole number that divides another whole number exactly.
Q6. What is important to understand about Common multiples?
Answer: A multiple is a result found by multiplying a number by a whole number.
Q7. What is important to understand about Least common multiple introduction?
Answer: A multiple is a result found by multiplying a number by a whole number.
Q8. What is important to understand about Prime numbers?
Answer: A prime number has exactly two positive factors: 1 and itself.
Q9. What is important to understand about Composite numbers?
Answer: A composite number has more than two positive factors.
Q10. What is important to understand about Prime factorization introduction?
Answer: A factor is a whole number that divides another whole number exactly.
Q11. What is important to understand about Factor trees?
Answer: A factor is a whole number that divides another whole number exactly.
Q12. What is important to understand about Grouping and schedule applications?
Answer: Grouping and schedule applications is a Grade 6 mathematics idea in Factors, Multiples, Prime, and Composite Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q13. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q14. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q15. Why do units matter?
Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.
Q16. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q17. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.
Q18. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q19. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q20. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.
Q21. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q22. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q23. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q24. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q25. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q26. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q27. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q28. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q29. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.
Q30. What does representing mathematics mean?
Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.