Divisibility Tests Worksheet :: A Transum Worksheet - Free Printable

Let's solve this step by step.

We are given a list of numbers and need to determine which of them are divisible by the numbers 2, 3, 4, 5, 6, 8, and 9. We'll go through each number and apply divisibility rules for each of these divisors.

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Divisibility Rules:

- 2: Number is even (last digit is 0, 2, 4, 6, or 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.

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Now let's evaluate each number:

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1. 12

- 2: Yes (even)
- 3: 1+2=3 → divisible by 3 → Yes
- 4: 12 ÷ 4 = 3 → Yes
- 5: No (doesn't end in 0 or 5)
- 6: Yes (div by 2 and 3)
- 8: 12 ÷ 8 = 1.5 → No
- 9: 1+2=3 → not divisible by 9 → No

✔ 2, 3, 4, 6

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2. 24

- 2: Yes (even)
- 3: 2+4=6 → divisible by 3 → Yes
- 4: 24 ÷ 4 = 6 → Yes
- 5: No
- 6: Yes
- 8: 24 ÷ 8 = 3 → Yes
- 9: 2+4=6 → no → No

✔ 2, 3, 4, 6, 8

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3. 31

- 2: No (odd)
- 3: 3+1=4 → not divisible by 3 → No
- 4: 31 ÷ 4 = 7.75 → No
- 5: No
- 6: No
- 8: 31 ÷ 8 = 3.875 → No
- 9: 3+1=4 → No

✘ None

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4. 52

- 2: Yes (even)
- 3: 5+2=7 → not divisible by 3 → No
- 4: 52 ÷ 4 = 13 → Yes
- 5: No
- 6: No (not div by 3)
- 8: 52 ÷ 8 = 6.5 → No
- 9: 5+2=7 → No

✔ 2, 4

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5. 68

- 2: Yes (even)
- 3: 6+8=14 → not div by 3 → No
- 4: 68 ÷ 4 = 17 → Yes
- 5: No
- 6: No
- 8: 68 ÷ 8 = 8.5 → No
- 9: 6+8=14 → No

✔ 2, 4

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6. 100

- 2: Yes (even)
- 3: 1+0+0=1 → No
- 4: 00 → 0 ÷ 4 = 0 → Yes
- 5: Yes (ends in 0)
- 6: No (not div by 3)
- 8: 100 ÷ 8 = 12.5 → No
- 9: 1+0+0=1 → No

✔ 2, 4, 5

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7. 155

- 2: No (odd)
- 3: 1+5+5=11 → not div by 3 → No
- 4: 55 ÷ 4 = 13.75 → No
- 5: Yes (ends in 5)
- 6: No
- 8: 155 ÷ 8 = 19.375 → No
- 9: 1+5+5=11 → No

✔ 5

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8. 200

- 2: Yes
- 3: 2+0+0=2 → No
- 4: 00 → 0 ÷ 4 = 0 → Yes
- 5: Yes (ends in 0)
- 6: No
- 8: 200 ÷ 8 = 25 → Yes
- 9: 2+0+0=2 → No

✔ 2, 4, 5, 8

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9. 250

- 2: Yes
- 3: 2+5+0=7 → No
- 4: 50 ÷ 4 = 12.5 → No
- 5: Yes
- 6: No
- 8: 250 ÷ 8 = 31.25 → No
- 9: 2+5+0=7 → No

✔ 2, 5

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10. 301

- 2: No (odd)
- 3: 3+0+1=4 → No
- 4: 01 → 1 ÷ 4 = 0.25 → No
- 5: No
- 6: No
- 8: 301 ÷ 8 = 37.625 → No
- 9: 3+0+1=4 → No

✘ None

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11. 368

- 2: Yes (even)
- 3: 3+6+8=17 → not div by 3 → No
- 4: 68 ÷ 4 = 17 → Yes
- 5: No
- 6: No
- 8: 368 ÷ 8 = 46 → Yes
- 9: 3+6+8=17 → No

✔ 2, 4, 8

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12. 725

- 2: No (odd)
- 3: 7+2+5=14 → No
- 4: 25 ÷ 4 = 6.25 → No
- 5: Yes (ends in 5)
- 6: No
- 8: 725 ÷ 8 = 90.625 → No
- 9: 7+2+5=14 → No

✔ 5

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13. 2456

- 2: Yes (even)
- 3: 2+4+5+6=17 → No
- 4: 56 ÷ 4 = 14 → Yes
- 5: No
- 6: No
- 8: 456 ÷ 8 = 57 → Yes
- 9: 2+4+5+6=17 → No

✔ 2, 4, 8

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14. 7281

- 2: No (odd)
- 3: 7+2+8+1=18 → divisible by 3 → Yes
- 4: 81 ÷ 4 = 20.25 → No
- 5: No
- 6: No (not even)
- 8: 281 ÷ 8 = 35.125 → No
- 9: 7+2+8+1=18 → divisible by 9 → Yes

✔ 3, 9

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15. 284657

- 2: No (odd)
- 3: 2+8+4+6+5+7 = 32 → 32 ÷ 3 = 10.666 → No
- 4: 57 ÷ 4 = 14.25 → No
- 5: No (doesn’t end in 0 or 5)
- 6: No
- 8: 657 ÷ 8 = 82.125 → No
- 9: 32 → not divisible by 9 → No

✘ None

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16. 123123

- 2: No (odd)
- 3: 1+2+3+1+2+3 = 12 → divisible by 3 → Yes
- 4: 23 ÷ 4 = 5.75 → No
- 5: No
- 6: No (not even)
- 8: 123 ÷ 8 = 15.375 → No
- 9: 1+2+3+1+2+3 = 12 → not divisible by 9 → No

✔ 3

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✔ Final Table:

| Number | 2 | 3 | 4 | 5 | 6 | 8 | 9 |
|----------|---|---|---|---|---|---|---|
| 12 | ✔ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ |
| 24 | ✔ | ✔ | ✔ | ✘ | ✔ | ✔ | ✘ |
| 31 | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ |
| 52 | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ |
| 68 | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ |
| 100 | ✔ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ |
| 155 | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ |
| 200 | ✔ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ |
| 250 | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ |
| 301 | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ |
| 368 | ✔ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ |
| 725 | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ |
| 2456 | ✔ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ |
| 7281 | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✔ |
| 284657 | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ |
| 123123 | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ |

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