Divisibility Rules Worksheets - Math Worksheets - MathsDiary.com - Free Printable

Let's go through the "Multiples and Factors Worksheet" step by step to verify the check marks for each number and explain why a number is divisible by 2, 3, 4, 5, 6, 9, or 10.

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🔍 Divisibility Rules (Quick Reference)

| Divisor | Rule |
|--------|------|
| 2 | Number ends in an even digit (0, 2, 4, 6, 8) |
| 3 | Sum of digits is divisible by 3 |
| 4 | Last two digits form a number divisible by 4 |
| 5 | Ends in 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 9 | Sum of digits is divisible by 9 |
| 10 | Ends in 0 |

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Now let’s analyze each number one by one.

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✔ 1. 45

- 2? → Ends in 5 → Odd → ✘
- 3? → 4 + 5 = 9 → 9 ÷ 3 = 3 → ✔
- 4? → Last two digits: 45 → 45 ÷ 4 = 11.25 → ✘
- 5? → Ends in 5 → ✔
- 6? → Must be divisible by 2 and 3 → Not divisible by 2 → ✘
- 9? → 4 + 5 = 9 → 9 ÷ 9 = 1 → ✔
- 10? → Doesn’t end in 0 → ✘

✔ Correct: 3, 5, 9 → ✔️ Matches worksheet

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✔ 2. 369

- 2? → Ends in 9 → Odd → ✘
- 3? → 3 + 6 + 9 = 18 → 18 ÷ 3 = 6 → ✔
- 4? → Last two digits: 69 → 69 ÷ 4 = 17.25 → ✘
- 5? → Ends in 9 → ✘
- 6? → Needs 2 and 3 → Not divisible by 2 → ✘
- 9? → 3 + 6 + 9 = 18 → 18 ÷ 9 = 2 → ✔
- 10? → Ends in 9 → ✘

✔ Correct: 3, 9 → ✔️ Matches worksheet

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✔ 3. 7,870

- 2? → Ends in 0 → Even → ✔
- 3? → 7 + 8 + 7 + 0 = 22 → 22 ÷ 3 ≈ 7.33 → ✘
- 4? → Last two digits: 70 → 70 ÷ 4 = 17.5 → ✘
- 5? → Ends in 0 → ✔
- 6? → Needs 2 and 3 → Has 2 but not 3 → ✘
- 9? → 7+8+7+0=22 → 22 ÷ 9 ≈ 2.44 → ✘
- 10? → Ends in 0 → ✔

✔ Correct: 2, 5, 10 → ✔️ Matches worksheet

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✔ 4. 1,976

- 2? → Ends in 6 → Even → ✔
- 3? → 1 + 9 + 7 + 6 = 23 → 23 ÷ 3 ≈ 7.67 → ✘
- 4? → Last two digits: 76 → 76 ÷ 4 = 19 → ✔
- 5? → Ends in 6 → ✘
- 6? → Needs 2 and 3 → Has 2 but not 3 → ✘
- 9? → 1+9+7+6=23 → 23 ÷ 9 ≈ 2.56 → ✘
- 10? → Ends in 6 → ✘

Wait! The worksheet has a checkmark under 2, but not under 4 — that’s wrong!

But wait — last two digits are 76, and 76 ÷ 4 = 19 → ✔ So it should be divisible by 4.

✘ Error in worksheet: It should have a checkmark under 4, but it doesn't.

Also, no checkmark under 3, 6, 9, 5, 10 — correct.

So:
- ✔ 2 → yes
- ✔ 4 → yes → missing checkmark
- ✘ 3, 5, 6, 9, 10 → correct

🔴 Mistake: Missing checkmark for 4

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✔ 5. 6,003

- 2? → Ends in 3 → Odd → ✘
- 3? → 6 + 0 + 0 + 3 = 9 → 9 ÷ 3 = 3 → ✔
- 4? → Last two digits: 03 → 3 ÷ 4 = 0.75 → ✘
- 5? → Ends in 3 → ✘
- 6? → Needs 2 and 3 → Not divisible by 2 → ✘
- 9? → 6+0+0+3=9 → 9 ÷ 9 = 1 → ✔
- 10? → Ends in 3 → ✘

✔ Correct: 3, 9 → ✔️ Matches worksheet

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✔ 6. 136

- 2? → Ends in 6 → Even → ✔
- 3? → 1 + 3 + 6 = 10 → 10 ÷ 3 ≈ 3.33 → ✘
- 4? → Last two digits: 36 → 36 ÷ 4 = 9 → ✔
- 5? → Ends in 6 → ✘
- 6? → Needs 2 and 3 → Has 2 but not 3 → ✘
- 9? → 1+3+6=10 → 10 ÷ 9 ≈ 1.11 → ✘
- 10? → Ends in 6 → ✘

✔ Correct: 2, 4 → ✔️ Matches worksheet

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✔ 7. 1,674

- 2? → Ends in 4 → Even → ✔
- 3? → 1 + 6 + 7 + 4 = 18 → 18 ÷ 3 = 6 → ✔
- 4? → Last two digits: 74 → 74 ÷ 4 = 18.5 → ✘
- 5? → Ends in 4 → ✘
- 6? → Needs 2 and 3 → Both satisfied → ✔
- 9? → 1+6+7+4=18 → 18 ÷ 9 = 2 → ✔
- 10? → Ends in 4 → ✘

✔ Correct: 2, 3, 6, 9 → ✔️ Matches worksheet

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✔ 8. 35,496

- 2? → Ends in 6 → Even → ✔
- 3? → 3 + 5 + 4 + 9 + 6 = 27 → 27 ÷ 3 = 9 → ✔
- 4? → Last two digits: 96 → 96 ÷ 4 = 24 → ✔
- 5? → Ends in 6 → ✘
- 6? → Needs 2 and 3 → Both → ✔
- 9? → 3+5+4+9+6=27 → 27 ÷ 9 = 3 → ✔
- 10? → Ends in 6 → ✘

✔ Correct: 2, 3, 4, 6, 9 → ✔️ Matches worksheet

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🚩 Summary of Errors

The only mistake in the worksheet is:

> 1,976 — should be divisible by 4, but no checkmark is present.

Let’s double-check:
- 1,976 → last two digits: 76
- 76 ÷ 4 = 19 → exactly → ✔ divisible by 4

So, the worksheet is missing a checkmark under 4 for 1,976.

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✔ Final Answer:

All checkmarks are correct except:

🔹 1,976 should have a checkmark under 4.

✔ Corrected version:
- 1,976 → divisible by 2 and 4 → ✔

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📝 Conclusion:

The worksheet is mostly accurate, but there is one error:
> ✘ Missing checkmark for 4 under 1,976

This is likely due to oversight. All other entries follow the divisibility rules correctly.

Let me know if you'd like a corrected version of the table!