Divisibility Rules worksheet for practicing divisibility by 2, 3, 6, and 9.

Let’s solve each question on the worksheet using divisibility rules. I’ll explain each rule and apply it to the given numbers.

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🔢 Divisibility Rules Recap:

- 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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## ✔ Let's go row by row:

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🟢 Row 1: Divisible by 2?

#### ➤ Is 83 divisible by 2?
- Last digit = 3 → odd → NOT divisible by 2
✔ Answer: no

#### ➤ Is 34 divisible by 2?
- Last digit = 4 → even → divisible by 2
✔ Answer: yes

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🟢 Row 2: Divisible by 3?

#### ➤ Is 72 divisible by 3?
- Sum of digits: 7 + 2 = 9 → 9 ÷ 3 = 3 → divisible by 3
✔ Answer: yes

#### ➤ Is 53 divisible by 3?
- Sum of digits: 5 + 3 = 8 → 8 ÷ 3 = 2 remainder 2 → not divisible
✔ Answer: no

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🟢 Row 3: Divisible by 6?

*(Remember: Must be divisible by both 2 AND 3)*

#### ➤ Is 92 divisible by 6?
- Check by 2: last digit = 2 → even → ✔ divisible by 2
- Check by 3: 9 + 2 = 11 → 11 ÷ 3 = 3 rem 2 → ✘ not divisible by 3
→ So, not divisible by 6
✔ Answer: no

#### ➤ Is 84 divisible by 6?
- Check by 2: last digit = 4 → even → ✔
- Check by 3: 8 + 4 = 12 → 12 ÷ 3 = 4 → ✔
→ So, divisible by 6
✔ Answer: yes

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🟢 Row 4: Divisible by 9?

#### ➤ Is 153 divisible by 9?
- Sum of digits: 1 + 5 + 3 = 9 → 9 ÷ 9 = 1 → ✔ divisible by 9
✔ Answer: yes

#### ➤ 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 (for each box):

| 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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📌 Summary for the worksheet:

You would circle or select:
- Top left: no
- Top right: yes
- Middle left: yes
- Middle right: no
- Bottom left (row 3): no
- Bottom right (row 3): yes
- Bottom left (row 4): yes
- Bottom right (row 4): yes

✔ All solved using basic divisibility rules — quick and efficient!

Let me know if you’d like a printable answer key or visual explanations!