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Chapter 8: Divisibility Rules

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Divisibility Rules in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Divisibility by 2 (Divisibility means one whole number can be divided by another with no remainder.)

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.

8.1 Divisibility by 2

Divisibility means one whole number can be divided by another with no remainder. 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 8,868 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 8,868 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 781 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 781 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: No

Worked Example 3

Problem: Is 8,230 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 8,230 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 8,494 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 8,494 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 5

Problem: Is 6,788 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 6,788 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 2,179 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 2,179 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: No

Worked Example 7

Problem: Is 1,910 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 1,910 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 4,730 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 4,730 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 9

Problem: Is 6,980 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 6,980 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 962 divisible by 2?

  1. Apply the divisibility rule for 2.
  2. Check whether 962 ÷ 2 has remainder 0.

Very beginner explanation: A number is divisible by 2 when division by 2 leaves no remainder.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Divisibility by 2. 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.

8.2 Divisibility by 3

Divisibility means one whole number can be divided by another with no remainder. 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 5,889 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 5,889 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 4,746 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 4,746 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 3

Problem: Is 1,206 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 1,206 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 809 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 809 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: No

Worked Example 5

Problem: Is 6,243 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 6,243 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 9,210 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 9,210 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 7

Problem: Is 5,400 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 5,400 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 434 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 434 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 3,240 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 3,240 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 278 divisible by 3?

  1. Apply the divisibility rule for 3.
  2. Check whether 278 ÷ 3 has remainder 0.

Very beginner explanation: A number is divisible by 3 when division by 3 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 3. 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.

8.3 Divisibility by 4

Divisibility means one whole number can be divided by another with no remainder. 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 4,108 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 4,108 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 3,677 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 3,677 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: No

Worked Example 3

Problem: Is 8,808 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 8,808 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 3,555 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 3,555 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: No

Worked Example 5

Problem: Is 9,824 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 9,824 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 5,733 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 5,733 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: No

Worked Example 7

Problem: Is 180 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 180 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 3,637 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 3,637 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 8,668 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 8,668 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 5,918 divisible by 4?

  1. Apply the divisibility rule for 4.
  2. Check whether 5,918 ÷ 4 has remainder 0.

Very beginner explanation: A number is divisible by 4 when division by 4 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 4. 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.

8.4 Divisibility by 5

Divisibility means one whole number can be divided by another with no remainder. 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 1,635 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 1,635 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 3,320 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 3,320 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 3

Problem: Is 4,440 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 4,440 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 4,919 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 4,919 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: No

Worked Example 5

Problem: Is 6,785 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 6,785 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 4,360 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 4,360 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 7

Problem: Is 1,145 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 1,145 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 6,871 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 6,871 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 4,300 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 4,300 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 5,802 divisible by 5?

  1. Apply the divisibility rule for 5.
  2. Check whether 5,802 ÷ 5 has remainder 0.

Very beginner explanation: A number is divisible by 5 when division by 5 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 5. 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.

8.5 Divisibility by 6

Divisibility means one whole number can be divided by another with no remainder. 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 5,826 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 5,826 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 8,312 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 8,312 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: No

Worked Example 3

Problem: Is 9,726 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 9,726 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 3,876 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 3,876 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: Yes

Worked Example 5

Problem: Is 5,286 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 5,286 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 325 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 325 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: No

Worked Example 7

Problem: Is 2,100 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 2,100 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 6,979 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 6,979 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 2,490 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 2,490 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 3,254 divisible by 6?

  1. Apply the divisibility rule for 6.
  2. Check whether 3,254 ÷ 6 has remainder 0.

Very beginner explanation: A number is divisible by 6 when division by 6 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 6. 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.

8.6 Divisibility by 8

Divisibility means one whole number can be divided by another with no remainder. 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 8,008 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 8,008 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 5,712 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 5,712 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: Yes

Worked Example 3

Problem: Is 8,200 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 8,200 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 3,359 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 3,359 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: No

Worked Example 5

Problem: Is 7,648 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 7,648 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 6,021 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 6,021 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: No

Worked Example 7

Problem: Is 7,752 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 7,752 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 9,069 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 9,069 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 4,872 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 4,872 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 6,382 divisible by 8?

  1. Apply the divisibility rule for 8.
  2. Check whether 6,382 ÷ 8 has remainder 0.

Very beginner explanation: A number is divisible by 8 when division by 8 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 8. 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.

8.7 Divisibility by 9

Divisibility means one whole number can be divided by another with no remainder. 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 2,979 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 2,979 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 9,499 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 9,499 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: No

Worked Example 3

Problem: Is 7,956 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 7,956 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 2,697 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 2,697 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: No

Worked Example 5

Problem: Is 243 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 243 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 3,594 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 3,594 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: No

Worked Example 7

Problem: Is 5,049 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 5,049 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 2,258 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 2,258 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 8,694 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 8,694 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 6,041 divisible by 9?

  1. Apply the divisibility rule for 9.
  2. Check whether 6,041 ÷ 9 has remainder 0.

Very beginner explanation: A number is divisible by 9 when division by 9 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 9. 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.

8.8 Divisibility by 10

Divisibility means one whole number can be divided by another with no remainder. 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 8,090 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 8,090 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: Yes

Worked Example 2

Problem: Is 8,436 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 8,436 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: No

Worked Example 3

Problem: Is 5,130 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 5,130 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: Yes

Worked Example 4

Problem: Is 9,901 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 9,901 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: No

Worked Example 5

Problem: Is 870 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 870 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: Yes

Worked Example 6

Problem: Is 437 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 437 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: No

Worked Example 7

Problem: Is 4,870 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 4,870 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: Yes

Worked Example 8

Problem: Is 1,775 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 1,775 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: No

Worked Example 9

Problem: Is 7,420 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 7,420 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: Yes

Worked Example 10

Problem: Is 7,742 divisible by 10?

  1. Apply the divisibility rule for 10.
  2. Check whether 7,742 ÷ 10 has remainder 0.

Very beginner explanation: A number is divisible by 10 when division by 10 leaves no remainder.

Answer: No

Practice Exercise

Create one new Grade 6 problem about Divisibility by 10. 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.

8.9 Using more than one divisibility rule

Divisibility means one whole number can be divided by another with no remainder. 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 Using more than one divisibility rule to analyze the values 12 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Using more than one divisibility rule to analyze the values 15 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Using more than one divisibility rule to analyze the values 11 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Using more than one divisibility rule to analyze the values 24 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Using more than one divisibility rule to analyze the values 29 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Using more than one divisibility rule to analyze the values 7 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Using more than one divisibility rule to analyze the values 10 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Using more than one divisibility rule to analyze the values 2 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Using more than one divisibility rule to analyze the values 9 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Using more than one divisibility rule to analyze the values 18 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Using more than one divisibility rule. 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.

8.10 Divisibility puzzles

Divisibility means one whole number can be divided by another with no remainder. 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 Divisibility puzzles to analyze the values 18 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Divisibility puzzles to analyze the values 7 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Divisibility puzzles to analyze the values 5 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Divisibility puzzles to analyze the values 18 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Divisibility puzzles to analyze the values 27 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Divisibility puzzles to analyze the values 16 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Divisibility puzzles to analyze the values 9 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Divisibility puzzles to analyze the values 13 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Divisibility puzzles to analyze the values 11 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Divisibility puzzles to analyze the values 14 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Divisibility means one whole number can be divided by another with no remainder.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Divisibility puzzles. 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.

8.11 Finding factors with divisibility rules

Divisibility means one whole number can be divided by another with no remainder. 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 80.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Worked Example 2

Problem: List all positive factors of 85.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 5, 17, 85

Worked Example 3

Problem: List all positive factors of 50.

  1. Test whole numbers that divide exactly.
  2. 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 4

Problem: List all positive factors of 80.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Worked Example 5

Problem: List all positive factors of 46.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 2, 23, 46

Worked Example 6

Problem: List all positive factors of 49.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 7, 49

Worked Example 7

Problem: List all positive factors of 28.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 2, 4, 7, 14, 28

Worked Example 8

Problem: List all positive factors of 51.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 3, 17, 51

Worked Example 9

Problem: List all positive factors of 56.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 2, 4, 7, 8, 14, 28, 56

Worked Example 10

Problem: List all positive factors of 69.

  1. Test whole numbers that divide exactly.
  2. Pair factors when their product equals the number.

Very beginner explanation: Factors divide a number with no remainder.

Answer: 1, 3, 23, 69

Practice Exercise

Create one new Grade 6 problem about Finding factors with divisibility rules. 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.

8.12 Checking divisibility efficiently

Divisibility means one whole number can be divided by another with no remainder. 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: A loop adds 2 exactly 4 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 8

Worked Example 2

Problem: A loop adds 4 exactly 3 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 12

Worked Example 3

Problem: A loop adds 4 exactly 9 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 36

Worked Example 4

Problem: A loop adds 3 exactly 5 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 15

Worked Example 5

Problem: A loop adds 4 exactly 9 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 36

Worked Example 6

Problem: A loop adds 5 exactly 4 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 20

Worked Example 7

Problem: A loop adds 5 exactly 4 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 20

Worked Example 8

Problem: A loop adds 4 exactly 9 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 36

Worked Example 9

Problem: A loop adds 4 exactly 6 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 24

Worked Example 10

Problem: A loop adds 3 exactly 4 times. What total is produced?

  1. Recognize repeated addition.
  2. Multiply the repeated amount by the number of repeats.

Very beginner explanation: Loops replace repeated instructions with one reusable rule.

Answer: 12

Practice Exercise

Create one new Grade 6 problem about Checking divisibility efficiently. 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.

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30 Review Questions and Answers

Q1. What is important to understand about Divisibility by 2?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q2. What is important to understand about Divisibility by 3?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q3. What is important to understand about Divisibility by 4?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q4. What is important to understand about Divisibility by 5?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q5. What is important to understand about Divisibility by 6?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q6. What is important to understand about Divisibility by 8?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q7. What is important to understand about Divisibility by 9?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q8. What is important to understand about Divisibility by 10?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q9. What is important to understand about Using more than one divisibility rule?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q10. What is important to understand about Divisibility puzzles?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q11. What is important to understand about Finding factors with divisibility rules?

Answer: Divisibility means one whole number can be divided by another with no remainder.

Q12. What is important to understand about Checking divisibility efficiently?

Answer: Divisibility means one whole number can be divided by another with no remainder.

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.