Divisibility Rules Worksheets - Math Monks - Free Printable

Let’s solve each problem using divisibility rules. The goal is to circle the numbers from the given list that divide the main number evenly (with no remainder).

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🔢 Divisibility Rules Quick Reference:

- 2: Last digit is even (0, 2, 4, 6, 8)
- 3: Sum of digits is divisible by 3
- 4: Last two digits form a number divisible by 4
- 5: Last digit is 0 or 5
- 6: Divisible by both 2 and 3
- 7: Double the last digit, subtract from the rest; if result is divisible by 7, so is original (or use direct division for small numbers)
- 8: Last three digits divisible by 8
- 9: Sum of digits divisible by 9
- 10: Last digit is 0
- 12: Divisible by both 3 and 4

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## ✔ Problem-by-Problem Solutions:

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1. 16,596 — Already done: circled 2, 3, 4, 12

✔ Check:
- Ends in 6 → divisible by 2
- Sum = 1+6+5+9+6 = 27 → divisible by 3
- Last two digits: 96 → 96 ÷ 4 = 24 → divisible by 4
- Since divisible by 3 and 4 → divisible by 12
- 7? 16596 ÷ 7 = 2370.857… → not divisible → correct not circled

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2. 82,176 — Options: 2, 4, 8, 10

✔ Check:
- Ends in 6 → divisible by 2
- Last two digits: 76 → 76 ÷ 4 = 19 → divisible by 4
- Last three digits: 176 → 176 ÷ 8 = 22 → divisible by 8
- Ends in 6, not 0 → not divisible by 10
→ Circle: 2, 4, 8

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3. 984 — Options: 3, 4, 5, 6

✔ Check:
- Sum = 9+8+4 = 21 → divisible by 3
- Last two digits: 84 → 84 ÷ 4 = 21 → divisible by 4
- Ends in 4, not 0 or 5 → not divisible by 5
- Divisible by 2 (even) and 3 → divisible by 6
→ Circle: 3, 4, 6

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4. 852 — Options: 2, 5, 8, 9, 12

✔ Check:
- Ends in 2 → divisible by 2
- Not ending in 0/5 → not divisible by 5
- Last three digits: 852 → 852 ÷ 8 = 106.5 → not divisible by 8
- Sum = 8+5+2 = 15 → not divisible by 9 → not divisible by 9
- Divisible by 2 and 3 (sum=15 → divisible by 3) → divisible by 12
→ Circle: 2, 12

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5. 225 — Options: 2, 5, 7, 10

✔ Check:
- Ends in 5 → not even → not divisible by 2
- Ends in 5 → divisible by 5
- 225 ÷ 7 = 32.14... → not divisible by 7
- Doesn’t end in 0 → not divisible by 10
→ Circle: 5

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6. 603,808 — Options: 2, 4, 5, 7

✔ Check:
- Ends in 8 → divisible by 2
- Last two digits: 08 → 8 ÷ 4 = 2 → divisible by 4
- Ends in 8, not 0/5 → not divisible by 5
- 603808 ÷ 7 = 86258.285... → not divisible by 7
→ Circle: 2, 4

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7. 8,176 — Options: 2, 3, 5, 8

✔ Check:
- Ends in 6 → divisible by 2
- Sum = 8+1+7+6 = 22 → 22 not divisible by 3 → not divisible by 3
- Ends in 6 → not 0/5 → not divisible by 5
- Last three digits: 176 → 176 ÷ 8 = 22 → divisible by 8
→ Circle: 2, 8

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8. 356 — Options: 2, 3, 4, 56

✔ Check:
- Ends in 6 → divisible by 2
- Sum = 3+5+6 = 14 → not divisible by 3 → not divisible by 3
- Last two digits: 56 → 56 ÷ 4 = 14 → divisible by 4
- Is 356 divisible by 56? 356 ÷ 56 ≈ 6.357 → not whole → not divisible by 56
→ Circle: 2, 4

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9. 16,596 — Same as #1! Options: 2, 3, 4, 7

✔ We already know:
- Divisible by 2, 3, 4
- 16596 ÷ 7 = 2370.857… → not divisible by 7
→ Circle: 2, 3, 4

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10. 9,942 — Options: 2, 3, 5, 6

✔ Check:
- Ends in 2 → divisible by 2
- Sum = 9+9+4+2 = 24 → divisible by 3
- Not ending in 0/5 → not divisible by 5
- Divisible by 2 and 3 → divisible by 6
→ Circle: 2, 3, 6

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11. 414 — Options: 2, 3, 6, 9

✔ Check:
- Ends in 4 → divisible by 2
- Sum = 4+1+4 = 9 → divisible by 3 and 9
- Divisible by 2 and 3 → divisible by 6
→ Circle: 2, 3, 6, 9

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12. 26,175 — Options: 2, 5, 7, 10

✔ Check:
- Ends in 5 → not even → not divisible by 2
- Ends in 5 → divisible by 5
- 26175 ÷ 7 = 3739.285... → not divisible by 7
- Doesn’t end in 0 → not divisible by 10
→ Circle: 5

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## 🟩 Final Answers (Circled Numbers):

| Problem | Circled Factors |
|---------|------------------|
| 1 | 2, 3, 4, 12 |
| 2 | 2, 4, 8 |
| 3 | 3, 4, 6 |
| 4 | 2, 12 |
| 5 | 5 |
| 6 | 2, 4 |
| 7 | 2, 8 |
| 8 | 2, 4 |
| 9 | 2, 3, 4 |
| 10 | 2, 3, 6 |
| 11 | 2, 3, 6, 9 |
| 12 | 5 |

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✔ You can now circle these on your worksheet!

Let me know if you want a printable version or explanation of any rule!