Divisibility test worksheet for numbers 2 through 9.
A math worksheet with a grid for determining divisibility of numbers by 2, 3, 4, 5, 6, 8, and 9, listing numbers like 12, 24, 31, 52, etc.
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Step-by-step solution for: Divisibility Tests Worksheet :: A Transum Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Divisibility Tests Worksheet :: A Transum Worksheet
To solve this problem, we need to check if each number on the left is divisible by the numbers at the top (2, 3, 4, 5, 6, 8, and 9).
Here are the quick rules to help us:
* Divisible by 2: The number ends in 0, 2, 4, 6, or 8 (it is even).
* Divisible by 3: Add all the digits together. If the sum is divisible by 3, the number is too.
* Divisible by 4: Look at the last two digits. If that two-digit number is divisible by 4, the whole number is.
* Divisible by 5: The number ends in 0 or 5.
* Divisible by 6: It must be divisible by BOTH 2 and 3.
* Divisible by 8: Look at the last three digits. If that three-digit number is divisible by 8, the whole number is.
* Divisible by 9: Add all the digits together. If the sum is divisible by 9, the number is too.
Let's go through each row step-by-step.
1. Number: 12
* 2: Yes (ends in 2).
* 3: Yes ($1+2=3$).
* 4: Yes (12 is divisible by 4).
* 5: No (doesn't end in 0 or 5).
* 6: Yes (divisible by 2 and 3).
* 8: No (12 is not divisible by 8).
* 9: No ($1+2=3$, not divisible by 9).
2. Number: 24
* 2: Yes (even).
* 3: Yes ($2+4=6$).
* 4: Yes (24 is divisible by 4).
* 5: No.
* 6: Yes (divisible by 2 and 3).
* 8: Yes (24 is divisible by 8).
* 9: No ($2+4=6$).
3. Number: 31
* 2: No (odd).
* 3: No ($3+1=4$).
* 4: No (31 is not divisible by 4).
* 5: No.
* 6: No.
* 8: No.
* 9: No.
*(31 is a prime number, so it is only divisible by 1 and itself).*
4. Number: 52
* 2: Yes (even).
* 3: No ($5+2=7$).
* 4: Yes (52 $\div$ 4 = 13).
* 5: No.
* 6: No (not divisible by 3).
* 8: No (52 $\div$ 8 = 6.5).
* 9: No.
5. Number: 68
* 2: Yes (even).
* 3: No ($6+8=14$).
* 4: Yes (68 $\div$ 4 = 17).
* 5: No.
* 6: No.
* 8: No (68 $\div$ 8 = 8.5).
* 9: No.
6. Number: 100
* 2: Yes (even).
* 3: No ($1+0+0=1$).
* 4: Yes (00 is divisible by 4).
* 5: Yes (ends in 0).
* 6: No.
* 8: No (100 $\div$ 8 = 12.5).
* 9: No.
7. Number: 155
* 2: No (odd).
* 3: No ($1+5+5=11$).
* 4: No (odd).
* 5: Yes (ends in 5).
* 6: No.
* 8: No.
* 9: No.
8. Number: 200
* 2: Yes (even).
* 3: No ($2+0+0=2$).
* 4: Yes (00 is divisible by 4).
* 5: Yes (ends in 0).
* 6: No.
* 8: Yes (200 $\div$ 8 = 25).
* 9: No.
9. Number: 250
* 2: Yes (even).
* 3: No ($2+5+0=7$).
* 4: No (50 is not divisible by 4; $4 \times 12=48$).
* 5: Yes (ends in 0).
* 6: No.
* 8: No (250 $\div$ 8 = 31.25).
* 9: No.
10. Number: 301
* 2: No (odd).
* 3: No ($3+0+1=4$).
* 4: No.
* 5: No.
* 6: No.
* 8: No.
* 9: No.
11. Number: 368
* 2: Yes (even).
* 3: No ($3+6+8=17$).
* 4: Yes (68 is divisible by 4).
* 5: No.
* 6: No.
* 8: Yes (368 $\div$ 8 = 46).
* 9: No.
12. Number: 725
* 2: No (odd).
* 3: No ($7+2+5=14$).
* 4: No.
* 5: Yes (ends in 5).
* 6: No.
* 8: No.
* 9: No.
13. Number: 2456
* 2: Yes (even).
* 3: No ($2+4+5+6=17$).
* 4: Yes (56 is divisible by 4).
* 5: No.
* 6: No.
* 8: Yes (456 $\div$ 8 = 57).
* 9: No.
14. Number: 7281
* 2: No (odd).
* 3: Yes ($7+2+8+1=18$, and 18 is divisible by 3).
* 4: No.
* 5: No.
* 6: No (must be even).
* 8: No (odd).
* 9: Yes ($7+2+8+1=18$, and 18 is divisible by 9).
15. Number: 284657
* 2: No (odd).
* 3: No ($2+8+4+6+5+7=32$, not divisible by 3).
* 4: No.
* 5: No (ends in 7).
* 6: No.
* 8: No.
* 9: No ($32$ is not divisible by 9).
16. Number: 123123
* 2: No (odd).
* 3: Yes ($1+2+3+1+2+3=12$, divisible by 3).
* 4: No.
* 5: No.
* 6: No (must be even).
* 8: No.
* 9: No ($12$ is not divisible by 9).
Final Answer:
| | 2 | 3 | 4 | 5 | 6 | 8 | 9 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 12 | Yes | Yes | Yes | No | Yes | No | No |
| 24 | Yes | Yes | Yes | No | Yes | Yes | No |
| 31 | No | No | No | No | No | No | No |
| 52 | Yes | No | Yes | No | No | No | No |
| 68 | Yes | No | Yes | No | No | No | No |
| 100 | Yes | No | Yes | Yes | No | No | No |
| 155 | No | No | No | Yes | No | No | No |
| 200 | Yes | No | Yes | Yes | No | Yes | No |
| 250 | Yes | No | No | Yes | No | No | No |
| 301 | No | No | No | No | No | No | No |
| 368 | Yes | No | Yes | No | No | Yes | No |
| 725 | No | No | No | Yes | No | No | No |
| 2456 | Yes | No | Yes | No | No | Yes | No |
| 7281 | No | Yes | No | No | No | No | Yes |
| 284657| No | No | No | No | No | No | No |
| 123123| No | Yes | No | No | No | No | No |
Here are the quick rules to help us:
* Divisible by 2: The number ends in 0, 2, 4, 6, or 8 (it is even).
* Divisible by 3: Add all the digits together. If the sum is divisible by 3, the number is too.
* Divisible by 4: Look at the last two digits. If that two-digit number is divisible by 4, the whole number is.
* Divisible by 5: The number ends in 0 or 5.
* Divisible by 6: It must be divisible by BOTH 2 and 3.
* Divisible by 8: Look at the last three digits. If that three-digit number is divisible by 8, the whole number is.
* Divisible by 9: Add all the digits together. If the sum is divisible by 9, the number is too.
Let's go through each row step-by-step.
1. Number: 12
* 2: Yes (ends in 2).
* 3: Yes ($1+2=3$).
* 4: Yes (12 is divisible by 4).
* 5: No (doesn't end in 0 or 5).
* 6: Yes (divisible by 2 and 3).
* 8: No (12 is not divisible by 8).
* 9: No ($1+2=3$, not divisible by 9).
2. Number: 24
* 2: Yes (even).
* 3: Yes ($2+4=6$).
* 4: Yes (24 is divisible by 4).
* 5: No.
* 6: Yes (divisible by 2 and 3).
* 8: Yes (24 is divisible by 8).
* 9: No ($2+4=6$).
3. Number: 31
* 2: No (odd).
* 3: No ($3+1=4$).
* 4: No (31 is not divisible by 4).
* 5: No.
* 6: No.
* 8: No.
* 9: No.
*(31 is a prime number, so it is only divisible by 1 and itself).*
4. Number: 52
* 2: Yes (even).
* 3: No ($5+2=7$).
* 4: Yes (52 $\div$ 4 = 13).
* 5: No.
* 6: No (not divisible by 3).
* 8: No (52 $\div$ 8 = 6.5).
* 9: No.
5. Number: 68
* 2: Yes (even).
* 3: No ($6+8=14$).
* 4: Yes (68 $\div$ 4 = 17).
* 5: No.
* 6: No.
* 8: No (68 $\div$ 8 = 8.5).
* 9: No.
6. Number: 100
* 2: Yes (even).
* 3: No ($1+0+0=1$).
* 4: Yes (00 is divisible by 4).
* 5: Yes (ends in 0).
* 6: No.
* 8: No (100 $\div$ 8 = 12.5).
* 9: No.
7. Number: 155
* 2: No (odd).
* 3: No ($1+5+5=11$).
* 4: No (odd).
* 5: Yes (ends in 5).
* 6: No.
* 8: No.
* 9: No.
8. Number: 200
* 2: Yes (even).
* 3: No ($2+0+0=2$).
* 4: Yes (00 is divisible by 4).
* 5: Yes (ends in 0).
* 6: No.
* 8: Yes (200 $\div$ 8 = 25).
* 9: No.
9. Number: 250
* 2: Yes (even).
* 3: No ($2+5+0=7$).
* 4: No (50 is not divisible by 4; $4 \times 12=48$).
* 5: Yes (ends in 0).
* 6: No.
* 8: No (250 $\div$ 8 = 31.25).
* 9: No.
10. Number: 301
* 2: No (odd).
* 3: No ($3+0+1=4$).
* 4: No.
* 5: No.
* 6: No.
* 8: No.
* 9: No.
11. Number: 368
* 2: Yes (even).
* 3: No ($3+6+8=17$).
* 4: Yes (68 is divisible by 4).
* 5: No.
* 6: No.
* 8: Yes (368 $\div$ 8 = 46).
* 9: No.
12. Number: 725
* 2: No (odd).
* 3: No ($7+2+5=14$).
* 4: No.
* 5: Yes (ends in 5).
* 6: No.
* 8: No.
* 9: No.
13. Number: 2456
* 2: Yes (even).
* 3: No ($2+4+5+6=17$).
* 4: Yes (56 is divisible by 4).
* 5: No.
* 6: No.
* 8: Yes (456 $\div$ 8 = 57).
* 9: No.
14. Number: 7281
* 2: No (odd).
* 3: Yes ($7+2+8+1=18$, and 18 is divisible by 3).
* 4: No.
* 5: No.
* 6: No (must be even).
* 8: No (odd).
* 9: Yes ($7+2+8+1=18$, and 18 is divisible by 9).
15. Number: 284657
* 2: No (odd).
* 3: No ($2+8+4+6+5+7=32$, not divisible by 3).
* 4: No.
* 5: No (ends in 7).
* 6: No.
* 8: No.
* 9: No ($32$ is not divisible by 9).
16. Number: 123123
* 2: No (odd).
* 3: Yes ($1+2+3+1+2+3=12$, divisible by 3).
* 4: No.
* 5: No.
* 6: No (must be even).
* 8: No.
* 9: No ($12$ is not divisible by 9).
Final Answer:
| | 2 | 3 | 4 | 5 | 6 | 8 | 9 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 12 | Yes | Yes | Yes | No | Yes | No | No |
| 24 | Yes | Yes | Yes | No | Yes | Yes | No |
| 31 | No | No | No | No | No | No | No |
| 52 | Yes | No | Yes | No | No | No | No |
| 68 | Yes | No | Yes | No | No | No | No |
| 100 | Yes | No | Yes | Yes | No | No | No |
| 155 | No | No | No | Yes | No | No | No |
| 200 | Yes | No | Yes | Yes | No | Yes | No |
| 250 | Yes | No | No | Yes | No | No | No |
| 301 | No | No | No | No | No | No | No |
| 368 | Yes | No | Yes | No | No | Yes | No |
| 725 | No | No | No | Yes | No | No | No |
| 2456 | Yes | No | Yes | No | No | Yes | No |
| 7281 | No | Yes | No | No | No | No | Yes |
| 284657| No | No | No | No | No | No | No |
| 123123| No | Yes | No | No | No | No | No |
Parent Tip: Review the logic above to help your child master the concept of divisibility test worksheet.
