Divisibility rules | parul_rajpal - Free Printable

Let's solve this step by step using divisibility rules for the numbers listed. We will check each number to see if it is divisible by 2, 3, 4, 5, 6, and 10.

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🔹 Divisibility Rules Recap:

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

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Now, let’s go through each number:

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#### 1. 637
- By 2? → Ends in 7 (odd) → ✘
- By 3? → 6+3+7 = 16 → 16 not divisible by 3 → ✘
- By 4? → Last two digits: 37 → 37 ÷ 4 = 9.25 → ✘
- By 5? → Ends in 7 → ✘
- By 6? → Not divisible by 2 or 3 → ✘
- By 10? → Doesn't end in 0 → ✘

✔ None

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#### 2. 303
- By 2? → Ends in 3 → ✘
- By 3? → 3+0+3 = 6 → 6 ÷ 3 = 2 → ✔
- By 4? → Last two digits: 03 → 3 ÷ 4 = 0.75 → ✘
- By 5? → Ends in 3 → ✘
- By 6? → Not divisible by 2 → ✘
- By 10? → No → ✘

✔ Only by 3

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#### 3. 756
- By 2? → Ends in 6 → ✔
- By 3? → 7+5+6 = 18 → 18 ÷ 3 = 6 → ✔
- By 4? → Last two digits: 56 → 56 ÷ 4 = 14 → ✔
- By 5? → Ends in 6 → ✘
- By 6? → Divisible by 2 and 3 → ✔
- By 10? → Ends in 6 → ✘

✔ By 2, 3, 4, 6

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#### 4. 1,455
- By 2? → Ends in 5 → ✘
- By 3? → 1+4+5+5 = 15 → 15 ÷ 3 = 5 → ✔
- By 4? → Last two digits: 55 → 55 ÷ 4 = 13.75 → ✘
- By 5? → Ends in 5 → ✔
- By 6? → Not divisible by 2 → ✘
- By 10? → No → ✘

✔ By 3, 5

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#### 5. 369
- By 2? → Ends in 9 → ✘
- By 3? → 3+6+9 = 18 → 18 ÷ 3 = 6 → ✔
- By 4? → Last two digits: 69 → 69 ÷ 4 = 17.25 → ✘
- By 5? → Ends in 9 → ✘
- By 6? → Not divisible by 2 → ✘
- By 10? → No → ✘

✔ Only by 3

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#### 6. 1,976
- By 2? → Ends in 6 → ✔
- By 3? → 1+9+7+6 = 23 → 23 not divisible by 3 → ✘
- By 4? → Last two digits: 76 → 76 ÷ 4 = 19 → ✔
- By 5? → Ends in 6 → ✘
- By 6? → Not divisible by 3 → ✘
- By 10? → No → ✘

✔ By 2, 4

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#### 7. 1,674
- By 2? → Ends in 4 → ✔
- By 3? → 1+6+7+4 = 18 → 18 ÷ 3 = 6 → ✔
- By 4? → Last two digits: 74 → 74 ÷ 4 = 18.5 → ✘
- By 5? → Ends in 4 → ✘
- By 6? → Divisible by 2 and 3 → ✔
- By 10? → No → ✘

✔ By 2, 3, 6

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#### 8. 6,005
- By 2? → Ends in 5 → ✘
- By 3? → 6+0+0+5 = 11 → 11 not divisible by 3 → ✘
- By 4? → Last two digits: 05 → 5 ÷ 4 = 1.25 → ✘
- By 5? → Ends in 5 → ✔
- By 6? → Not divisible by 2 or 3 → ✘
- By 10? → No → ✘

✔ Only by 5

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#### 9. 7,870
- By 2? → Ends in 0 → ✔
- By 3? → 7+8+7+0 = 22 → 22 not divisible by 3 → ✘
- By 4? → Last two digits: 70 → 70 ÷ 4 = 17.5 → ✘
- By 5? → Ends in 0 → ✔
- By 6? → Not divisible by 3 → ✘
- By 10? → Ends in 0 → ✔

✔ By 2, 5, 10

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#### 10. 35,496
- By 2? → Ends in 6 → ✔
- By 3? → 3+5+4+9+6 = 27 → 27 ÷ 3 = 9 → ✔
- By 4? → Last two digits: 96 → 96 ÷ 4 = 24 → ✔
- By 5? → Ends in 6 → ✘
- By 6? → Divisible by 2 and 3 → ✔
- By 10? → No → ✘

✔ By 2, 3, 4, 6

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#### 11. 8778
- By 2? → Ends in 8 → ✔
- By 3? → 8+7+7+8 = 30 → 30 ÷ 3 = 10 → ✔
- By 4? → Last two digits: 78 → 78 ÷ 4 = 19.5 → ✘
- By 5? → Ends in 8 → ✘
- By 6? → Divisible by 2 and 3 → ✔
- By 10? → No → ✘

✔ By 2, 3, 6

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#### 12. 4300
- By 2? → Ends in 0 → ✔
- By 3? → 4+3+0+0 = 7 → 7 not divisible by 3 → ✘
- By 4? → Last two digits: 00 → 0 ÷ 4 = 0 → ✔
- By 5? → Ends in 0 → ✔
- By 6? → Not divisible by 3 → ✘
- By 10? → Ends in 0 → ✔

✔ By 2, 4, 5, 10

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#### 13. 1033
- By 2? → Ends in 3 → ✘
- By 3? → 1+0+3+3 = 7 → 7 not divisible by 3 → ✘
- By 4? → Last two digits: 33 → 33 ÷ 4 = 8.25 → ✘
- By 5? → Ends in 3 → ✘
- By 6? → Not divisible by 2 or 3 → ✘
- By 10? → No → ✘

✔ None

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#### 14. 2940
- By 2? → Ends in 0 → ✔
- By 3? → 2+9+4+0 = 15 → 15 ÷ 3 = 5 → ✔
- By 4? → Last two digits: 40 → 40 ÷ 4 = 10 → ✔
- By 5? → Ends in 0 → ✔
- By 6? → Divisible by 2 and 3 → ✔
- By 10? → Ends in 0 → ✔

✔ All except possibly none — YES, all!

So: By 2, 3, 4, 5, 6, 10

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✔ Final Answer Table:

| Number | By 2 | By 3 | By 4 | By 5 | By 6 | By 10 |
|--------|------|------|------|------|------|-------|
| 637 | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ |
| 303 | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ |
| 756 | ✔ | ✔ | ✔ | ✘ | ✔ | ✘ |
| 1,455 | ✘ | ✔ | ✘ | ✔ | ✘ | ✘ |
| 369 | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ |
| 1,976 | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ |
| 1,674 | ✔ | ✔ | ✘ | ✘ | ✔ | ✘ |
| 6,005 | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ |
| 7,870 | ✔ | ✘ | ✘ | ✔ | ✘ | ✔ |
| 35,496 | ✔ | ✔ | ✔ | ✘ | ✔ | ✘ |
| 8778 | ✔ | ✔ | ✘ | ✘ | ✔ | ✘ |
| 4300 | ✔ | ✘ | ✔ | ✔ | ✘ | ✔ |
| 1033 | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ |
| 2940 | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |

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📝 Summary:

We used divisibility rules instead of actual division to quickly determine divisibility.

✔ Key Takeaway: These rules help us test large numbers without doing long division!

Let me know if you'd like this as a printable table or PDF.