Divisibility test worksheet - Free Printable

To solve this divisibility test, we need to check each number in the left column against the divisors in the top row (2, 3, 4, 5, 6, 9, 10). We will write YES if the number divides evenly (no remainder) and NO if it does not.

Here are the quick rules we will use:
* 2: The number is even (ends in 0, 2, 4, 6, 8).
* 3: Add up all the digits. If the sum is divisible by 3, the number is divisible by 3.
* 4: Look at the last two digits. If that two-digit number is divisible by 4, the whole number is.
* 5: The number ends in 0 or 5.
* 6: The number must be divisible by BOTH 2 and 3.
* 9: Add up all the digits. If the sum is divisible by 9, the number is divisible by 9.
* 10: The number ends in 0.

Let's go through each row step-by-step:

Row 1: Number 90
* 2: Ends in 0 (even). -> YES
* 3: $9 + 0 = 9$. 9 is divisible by 3. -> YES
* 4: Last two digits are 90. $90 \div 4 = 22.5$ (not whole). -> NO
* 5: Ends in 0. -> YES
* 6: Divisible by 2? Yes. Divisible by 3? Yes. -> YES
* 9: Sum of digits is 9. Divisible by 9. -> YES
* 10: Ends in 0. -> YES

Row 2: Number 88
* 2: Ends in 8 (even). -> YES
* 3: $8 + 8 = 16$. 16 is not divisible by 3. -> NO
* 4: Last two digits are 88. $88 \div 4 = 22$. -> YES
* 5: Does not end in 0 or 5. -> NO
* 6: Not divisible by 3, so not by 6. -> NO
* 9: Sum is 16. Not divisible by 9. -> NO
* 10: Does not end in 0. -> NO

Row 3: Number 75
* 2: Ends in 5 (odd). -> NO
* 3: $7 + 5 = 12$. 12 is divisible by 3. -> YES
* 4: Last two digits are 75. 75 is odd, so no. -> NO
* 5: Ends in 5. -> YES
* 6: Not divisible by 2. -> NO
* 9: Sum is 12. Not divisible by 9. -> NO
* 10: Does not end in 0. -> NO

Row 4: Number 16
* 2: Ends in 6 (even). -> YES
* 3: $1 + 6 = 7$. Not divisible by 3. -> NO
* 4: Last two digits are 16. $16 \div 4 = 4$. -> YES
* 5: Does not end in 0 or 5. -> NO
* 6: Not divisible by 3. -> NO
* 9: Sum is 7. Not divisible by 9. -> NO
* 10: Does not end in 0. -> NO

Row 5: Number 87
* 2: Ends in 7 (odd). -> NO
* 3: $8 + 7 = 15$. 15 is divisible by 3. -> YES
* 4: Last two digits are 87. Odd number. -> NO
* 5: Does not end in 0 or 5. -> NO
* 6: Not divisible by 2. -> NO
* 9: Sum is 15. Not divisible by 9. -> NO
* 10: Does not end in 0. -> NO

Row 6: Number 27
* 2: Ends in 7 (odd). -> NO
* 3: $2 + 7 = 9$. Divisible by 3. -> YES
* 4: Last two digits are 27. Odd number. -> NO
* 5: Does not end in 0 or 5. -> NO
* 6: Not divisible by 2. -> NO
* 9: Sum is 9. Divisible by 9. -> YES
* 10: Does not end in 0. -> NO

Row 7: Number 70
* 2: Ends in 0 (even). -> YES
* 3: $7 + 0 = 7$. Not divisible by 3. -> NO
* 4: Last two digits are 70. $70 \div 4 = 17.5$. -> NO
* 5: Ends in 0. -> YES
* 6: Not divisible by 3. -> NO
* 9: Sum is 7. Not divisible by 9. -> NO
* 10: Ends in 0. -> YES

Row 8: Number 84
* 2: Ends in 4 (even). -> YES
* 3: $8 + 4 = 12$. Divisible by 3. -> YES
* 4: Last two digits are 84. $84 \div 4 = 21$. -> YES
* 5: Does not end in 0 or 5. -> NO
* 6: Divisible by 2? Yes. By 3? Yes. -> YES
* 9: Sum is 12. Not divisible by 9. -> NO
* 10: Does not end in 0. -> NO

Row 9: Number 99
* 2: Ends in 9 (odd). -> NO
* 3: $9 + 9 = 18$. Divisible by 3. -> YES
* 4: Last two digits are 99. Odd number. -> NO
* 5: Does not end in 0 or 5. -> NO
* 6: Not divisible by 2. -> NO
* 9: Sum is 18. Divisible by 9. -> YES
* 10: Does not end in 0. -> NO

Row 10: Number 52
* 2: Ends in 2 (even). -> YES
* 3: $5 + 2 = 7$. Not divisible by 3. -> NO
* 4: Last two digits are 52. $52 \div 4 = 13$. -> YES
* 5: Does not end in 0 or 5. -> NO
* 6: Not divisible by 3. -> NO
* 9: Sum is 7. Not divisible by 9. -> NO
* 10: Does not end in 0. -> NO

Final Answer:

| | 2 | 3 | 4 | 5 | 6 | 9 | 10 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 90 | YES | YES | NO | YES | YES | YES | YES |
| 88 | YES | NO | YES | NO | NO | NO | NO |
| 75 | NO | YES | NO | YES | NO | NO | NO |
| 16 | YES | NO | YES | NO | NO | NO | NO |
| 87 | NO | YES | NO | NO | NO | NO | NO |
| 27 | NO | YES | NO | NO | NO | YES | NO |
| 70 | YES | NO | NO | YES | NO | NO | YES |
| 84 | YES | YES | YES | NO | YES | NO | NO |
| 99 | NO | YES | NO | NO | NO | YES | NO |
| 52 | YES | NO | YES | NO | NO | NO | NO |