Divisibility Worksheet Number Digit Sum 2 3 4 5 6 8 9 10 Number ... - Free Printable

Let's solve this Divisibility Worksheet step by step. The goal is to determine whether each number in the list is divisible by 2, 3, 4, 5, 6, 8, 9, and 10.

We'll go through each number one by one, apply the divisibility rules (as listed at the bottom), and fill out the table accordingly.

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🔢 Divisibility Rules Recap:

- 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
- 8: Last three digits form a number divisible by 8
- 9: Sum of digits is divisible by 9
- 10: Last digit is 0

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We are given the first row as an example:

| Number | Digit Sum | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | Divisible by: |
|--------|-----------|---|---|---|---|---|---|---|---|------|
| 1248 | 1+2+4+8=15 | Y | Y | Y | N | Y | N | N | N | 2, 3, 4, and 6 |

Let’s verify:
- 1248 → last digit = 8 → divisible by 2 ✔
- Digit sum = 15 → divisible by 3 ✔
- Last two digits: 48 → 48 ÷ 4 = 12 → divisible by 4 ✔
- Last digit ≠ 0 or 5 → not divisible by 5 ✘
- Divisible by 2 and 3 → divisible by 6 ✔
- Last three digits: 248 → 248 ÷ 8 = 31 → divisible by 8 ✔? Wait — 8×31=248 → yes! So should be Y, but it says N in the worksheet?

Wait — there’s a mistake in the provided example!

Let’s check:
- 1248 ÷ 8 = 156 → exactly → so it is divisible by 8.
- But the table says "N" for 8 → that’s incorrect.

But let's continue with the correct logic.

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Now we’ll process all numbers.

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✔ Step-by-step Solutions:

We will compute:
- Digit Sum
- Check each rule

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#### 1. 15
- Digit sum: 1 + 5 = 6
- 2: last digit 5 → odd → N
- 3: 6 ÷ 3 = 2 → Y
- 4: last two digits 15 → 15 ÷ 4 = 3.75 → N
- 5: ends in 5 → Y
- 6: must be divisible by 2 and 3 → 2 fails → N
- 8: last three digits = 015 → 15 ÷ 8 = 1.875 → N
- 9: 6 ÷ 9 → no → N
- 10: doesn't end in 0 → N

→ Divisible by: 3, 5

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#### 2. 16
- Digit sum: 1 + 6 = 7
- 2: ends in 6 → Y
- 3: 7 ÷ 3 → not divisible → N
- 4: 16 ÷ 4 = 4 → Y
- 5: ends in 6 → N
- 6: needs 2 and 3 → 3 fails → N
- 8: 16 ÷ 8 = 2 → Y
- 9: 7 ÷ 9 → no → N
- 10: ends in 6 → N

→ Divisible by: 2, 4, 8

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#### 3. 27
- Digit sum: 2 + 7 = 9
- 2: ends in 7 → odd → N
- 3: 9 ÷ 3 = 3 → Y
- 4: 27 ÷ 4 = 6.75 → N
- 5: ends in 7 → N
- 6: needs 2 and 3 → 2 fails → N
- 8: 27 ÷ 8 = 3.375 → N
- 9: 9 ÷ 9 = 1 → Y
- 10: ends in 7 → N

→ Divisible by: 3, 9

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#### 4. 28
- Digit sum: 2 + 8 = 10
- 2: ends in 8 → Y
- 3: 10 ÷ 3 ≈ 3.33 → N
- 4: 28 ÷ 4 = 7 → Y
- 5: ends in 8 → N
- 6: 2 and 3 → 3 fails → N
- 8: 28 ÷ 8 = 3.5 → N
- 9: 10 ÷ 9 → no → N
- 10: ends in 8 → N

→ Divisible by: 2, 4

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#### 5. 36
- Digit sum: 3 + 6 = 9
- 2: ends in 6 → Y
- 3: 9 ÷ 3 = 3 → Y
- 4: 36 ÷ 4 = 9 → Y
- 5: ends in 6 → N
- 6: 2 and 3 → both YES → Y
- 8: 36 ÷ 8 = 4.5 → N
- 9: 9 ÷ 9 = 1 → Y
- 10: ends in 6 → N

→ Divisible by: 2, 3, 4, 6, 9

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#### 6. 57
- Digit sum: 5 + 7 = 12
- 2: ends in 7 → N
- 3: 12 ÷ 3 = 4 → Y
- 4: 57 ÷ 4 = 14.25 → N
- 5: ends in 7 → N
- 6: 2 fails → N
- 8: 57 ÷ 8 = 7.125 → N
- 9: 12 ÷ 9 → no → N
- 10: ends in 7 → N

→ Divisible by: 3

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#### 7. 70
- Digit sum: 7 + 0 = 7
- 2: ends in 0 → Y
- 3: 7 ÷ 3 → no → N
- 4: 70 ÷ 4 = 17.5 → N
- 5: ends in 0 → Y
- 6: 2 and 3 → 3 fails → N
- 8: 70 ÷ 8 = 8.75 → N
- 9: 7 ÷ 9 → no → N
- 10: ends in 0 → Y

→ Divisible by: 2, 5, 10

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#### 8. 75
- Digit sum: 7 + 5 = 12
- 2: ends in 5 → odd → N
- 3: 12 ÷ 3 = 4 → Y
- 4: 75 ÷ 4 = 18.75 → N
- 5: ends in 5 → Y
- 6: 2 fails → N
- 8: 75 ÷ 8 = 9.375 → N
- 9: 12 ÷ 9 → no → N
- 10: ends in 5 → N

→ Divisible by: 3, 5

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#### 9. 91
- Digit sum: 9 + 1 = 10
- 2: ends in 1 → odd → N
- 3: 10 ÷ 3 → no → N
- 4: 91 ÷ 4 = 22.75 → N
- 5: ends in 1 → N
- 6: 2 and 3 → both fail → N
- 8: 91 ÷ 8 = 11.375 → N
- 9: 10 ÷ 9 → no → N
- 10: ends in 1 → N

→ Not divisible by any → none

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#### 10. 93
- Digit sum: 9 + 3 = 12
- 2: ends in 3 → odd → N
- 3: 12 ÷ 3 = 4 → Y
- 4: 93 ÷ 4 = 23.25 → N
- 5: ends in 3 → N
- 6: 2 fails → N
- 8: 93 ÷ 8 = 11.625 → N
- 9: 12 ÷ 9 → no → N
- 10: ends in 3 → N

→ Divisible by: 3

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#### 11. 102
- Digit sum: 1 + 0 + 2 = 3
- 2: ends in 2 → Y
- 3: 3 ÷ 3 = 1 → Y
- 4: 02 = 2 → 2 ÷ 4 = 0.5 → N
- 5: ends in 2 → N
- 6: 2 and 3 → both YES → Y
- 8: 102 ÷ 8 = 12.75 → N
- 9: 3 ÷ 9 → no → N
- 10: ends in 2 → N

→ Divisible by: 2, 3, 6

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#### 12. 144
- Digit sum: 1 + 4 + 4 = 9
- 2: ends in 4 → Y
- 3: 9 ÷ 3 = 3 → Y
- 4: 44 ÷ 4 = 11 → Y
- 5: ends in 4 → N
- 6: 2 and 3 → both YES → Y
- 8: 144 ÷ 8 = 18 → Y
- 9: 9 ÷ 9 = 1 → Y
- 10: ends in 4 → N

→ Divisible by: 2, 3, 4, 6, 8, 9

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#### 13. 150
- Digit sum: 1 + 5 + 0 = 6
- 2: ends in 0 → Y
- 3: 6 ÷ 3 = 2 → Y
- 4: 50 ÷ 4 = 12.5 → N
- 5: ends in 0 → Y
- 6: 2 and 3 → YES → Y
- 8: 150 ÷ 8 = 18.75 → N
- 9: 6 ÷ 9 → no → N
- 10: ends in 0 → Y

→ Divisible by: 2, 3, 5, 6, 10

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#### 14. 168
- Digit sum: 1 + 6 + 8 = 15
- 2: ends in 8 → Y
- 3: 15 ÷ 3 = 5 → Y
- 4: 68 ÷ 4 = 17 → Y
- 5: ends in 8 → N
- 6: 2 and 3 → YES → Y
- 8: 168 ÷ 8 = 21 → Y
- 9: 15 ÷ 9 → no → N
- 10: ends in 8 → N

→ Divisible by: 2, 3, 4, 6, 8

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#### 15. 195
- Digit sum: 1 + 9 + 5 = 15
- 2: ends in 5 → odd → N
- 3: 15 ÷ 3 = 5 → Y
- 4: 95 ÷ 4 = 23.75 → N
- 5: ends in 5 → Y
- 6: 2 fails → N
- 8: 195 ÷ 8 = 24.375 → N
- 9: 15 ÷ 9 → no → N
- 10: ends in 5 → N

→ Divisible by: 3, 5

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#### 16. 225
- Digit sum: 2 + 2 + 5 = 9
- 2: ends in 5 → odd → N
- 3: 9 ÷ 3 = 3 → Y
- 4: 25 ÷ 4 = 6.25 → N
- 5: ends in 5 → Y
- 6: 2 fails → N
- 8: 225 ÷ 8 = 28.125 → N
- 9: 9 ÷ 9 = 1 → Y
- 10: ends in 5 → N

→ Divisible by: 3, 5, 9

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#### 17. 256
- Digit sum: 2 + 5 + 6 = 13
- 2: ends in 6 → Y
- 3: 13 ÷ 3 → no → N
- 4: 56 ÷ 4 = 14 → Y
- 5: ends in 6 → N
- 6: 2 and 3 → 3 fails → N
- 8: 256 ÷ 8 = 32 → Y
- 9: 13 ÷ 9 → no → N
- 10: ends in 6 → N

→ Divisible by: 2, 4, 8

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#### 18. 268
- Digit sum: 2 + 6 + 8 = 16
- 2: ends in 8 → Y
- 3: 16 ÷ 3 → no → N
- 4: 68 ÷ 4 = 17 → Y
- 5: ends in 8 → N
- 6: 2 and 3 → 3 fails → N
- 8: 268 ÷ 8 = 33.5 → N
- 9: 16 ÷ 9 → no → N
- 10: ends in 8 → N

→ Divisible by: 2, 4

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#### 19. 316
- Digit sum: 3 + 1 + 6 = 10
- 2: ends in 6 → Y
- 3: 10 ÷ 3 → no → N
- 4: 16 ÷ 4 = 4 → Y
- 5: ends in 6 → N
- 6: 2 and 3 → 3 fails → N
- 8: 316 ÷ 8 = 39.5 → N
- 9: 10 ÷ 9 → no → N
- 10: ends in 6 → N

→ Divisible by: 2, 4

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#### 20. 450
- Digit sum: 4 + 5 + 0 = 9
- 2: ends in 0 → Y
- 3: 9 ÷ 3 = 3 → Y
- 4: 50 ÷ 4 = 12.5 → N
- 5: ends in 0 → Y
- 6: 2 and 3 → YES → Y
- 8: 450 ÷ 8 = 56.25 → N
- 9: 9 ÷ 9 = 1 → Y
- 10: ends in 0 → Y

→ Divisible by: 2, 3, 5, 6, 9, 10

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#### 21. 549
- Digit sum: 5 + 4 + 9 = 18
- 2: ends in 9 → odd → N
- 3: 18 ÷ 3 = 6 → Y
- 4: 49 ÷ 4 = 12.25 → N
- 5: ends in 9 → N
- 6: 2 fails → N
- 8: 549 ÷ 8 = 68.625 → N
- 9: 18 ÷ 9 = 2 → Y
- 10: ends in 9 → N

→ Divisible by: 3, 9

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#### 22. 1470
- Digit sum: 1 + 4 + 7 + 0 = 12
- 2: ends in 0 → Y
- 3: 12 ÷ 3 = 4 → Y
- 4: 70 ÷ 4 = 17.5 → N
- 5: ends in 0 → Y
- 6: 2 and 3 → YES → Y
- 8: 470 ÷ 8 = 58.75 → N
- 9: 12 ÷ 9 → no → N
- 10: ends in 0 → Y

→ Divisible by: 2, 3, 5, 6, 10

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#### 23. 4518
- Digit sum: 4 + 5 + 1 + 8 = 18
- 2: ends in 8 → Y
- 3: 18 ÷ 3 = 6 → Y
- 4: 18 ÷ 4 = 4.5 → N
- 5: ends in 8 → N
- 6: 2 and 3 → YES → Y
- 8: 518 ÷ 8 = 64.75 → N
- 9: 18 ÷ 9 = 2 → Y
- 10: ends in 8 → N

→ Divisible by: 2, 3, 6, 9

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#### 24. 7120
- Digit sum: 7 + 1 + 2 + 0 = 10
- 2: ends in 0 → Y
- 3: 10 ÷ 3 → no → N
- 4: 20 ÷ 4 = 5 → Y
- 5: ends in 0 → Y
- 6: 2 and 3 → 3 fails → N
- 8: 120 ÷ 8 = 15 → Y
- 9: 10 ÷ 9 → no → N
- 10: ends in 0 → Y

→ Divisible by: 2, 4, 5, 8, 10

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✔ Final Table (Completed):

| Number | Digit Sum | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | Divisible by: |
|--------|-----------|---|---|---|---|---|---|---|---|----------|
| 1248 | 15 | Y | Y | Y | N | Y | Y | N | N | 2, 3, 4, 6, 8 |
| 15 | 6 | N | Y | N | Y | N | N | N | N | 3, 5 |
| 16 | 7 | Y | N | Y | N | N | Y | N | N | 2, 4, 8 |
| 27 | 9 | N | Y | N | N | N | N | Y | N | 3, 9 |
| 28 | 10 | Y | N | Y | N | N | N | N | N | 2, 4 |
| 36 | 9 | Y | Y | Y | N | Y | N | Y | N | 2, 3, 4, 6, 9 |
| 57 | 12 | N | Y | N | N | N | N | N | N | 3 |
| 70 | 7 | Y | N | N | Y | N | N | N | Y | 2, 5, 10 |
| 75 | 12 | N | Y | N | Y | N | N | N | N | 3, 5 |
| 91 | 10 | N | N | N | N | N | N | N | N | none |
| 93 | 12 | N | Y | N | N | N | N | N | N | 3 |
| 102 | 3 | Y | Y | N | N | Y | N | N | N | 2, 3, 6 |
| 144 | 9 | Y | Y | Y | N | Y | Y | Y | N | 2, 3, 4, 6, 8, 9 |
| 150 | 6 | Y | Y | N | Y | Y | N | N | Y | 2, 3, 5, 6, 10 |
| 168 | 15 | Y | Y | Y | N | Y | Y | N | N | 2, 3, 4, 6, 8 |
| 195 | 15 | N | Y | N | Y | N | N | N | N | 3, 5 |
| 225 | 9 | N | Y | N | Y | N | N | Y | N | 3, 5, 9 |
| 256 | 13 | Y | N | Y | N | N | Y | N | N | 2, 4, 8 |
| 268 | 16 | Y | N | Y | N | N | N | N | N | 2, 4 |
| 316 | 10 | Y | N | Y | N | N | N | N | N | 2, 4 |
| 450 | 9 | Y | Y | N | Y | Y | N | Y | Y | 2, 3, 5, 6, 9, 10 |
| 549 | 18 | N | Y | N | N | N | N | Y | N | 3, 9 |
| 1470 | 12 | Y | Y | N | Y | Y | N | N | Y | 2, 3, 5, 6, 10 |
| 4518 | 18 | Y | Y | N | N | Y | N | Y | N | 2, 3, 6, 9 |
| 7120 | 10 | Y | N | Y | Y | N | Y | N | Y | 2, 4, 5, 8, 10 |

> ✔ Note: In the original example, 1248 was marked as not divisible by 8, but it is (1248 ÷ 8 = 156). That was likely a typo.

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📝 Summary:

This worksheet helps practice divisibility rules for numbers 2 through 10. Each number is tested using simple arithmetic and digit patterns.

Let me know if you'd like this as a printable PDF or want explanations for specific numbers!