4 Divisibility Rules Every Student Should Master with FREEBIES - Free Printable

Let's solve each question using divisibility rules. I'll go step by step and explain the reasoning for each.

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🔹 Divisibility Rules Quick Review:

- By 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
- By 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- By 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- By 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

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Now, let’s evaluate each question:

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1. Is 83 divisible by 2?

- Last digit: 3 → odd
- Not divisible by 2
✔ Answer: no

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2. Is 34 divisible by 2?

- Last digit: 4 → even
- Divisible by 2
✔ Answer: yes

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3. Is 72 divisible by 3?

- Sum of digits: 7 + 2 = 9
- 9 ÷ 3 = 3 → divisible by 3
✔ Answer: yes

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4. Is 53 divisible by 3?

- Sum of digits: 5 + 3 = 8
- 8 is not divisible by 3
✔ Answer: no

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5. Is 92 divisible by 6?

- Check divisibility by 2 and 3:
- Last digit: 2 → even → divisible by 2 ✔
- Sum of digits: 9 + 2 = 11 → 11 not divisible by 3 ✘
- Since not divisible by 3 → not divisible by 6
✔ Answer: no

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6. Is 84 divisible by 6?

- Last digit: 4 → even → divisible by 2 ✔
- Sum of digits: 8 + 4 = 12 → 12 ÷ 3 = 4 → divisible by 3 ✔
- So divisible by both 2 and 3 → divisible by 6
✔ Answer: yes

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7. Is 153 divisible by 9?

- Sum of digits: 1 + 5 + 3 = 9
- 9 ÷ 9 = 1 → divisible by 9
✔ Answer: yes

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8. Is 117 divisible by 9?

- Sum of digits: 1 + 1 + 7 = 9
- 9 ÷ 9 = 1 → divisible by 9
✔ Answer: yes

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| Is 83 divisible by 2? | no |
| Is 34 divisible by 2? | yes |
| Is 72 divisible by 3? | yes |
| Is 53 divisible by 3? | no |
| Is 92 divisible by 6? | no |
| Is 84 divisible by 6? | yes |
| Is 153 divisible by 9? | yes |
| Is 117 divisible by 9? | yes |

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You can now fill in the boxes accordingly! 🎉