Arithmetic & Numbers
Divisibility Rules Calculator
Enter a whole number. The calculator applies each divisibility rule — last digit, last two or three digits, digit sum — and tells you which divisors work and why.
- Digit sum 12
Step-by-step working 2 steps
- 1Apply each divisibility rule
÷ 2: yes (last digit 6 is even) ÷ 3: yes (digit sum 12) ÷ 4: yes (last two digits 36) ÷ 5: no (last digit 6) ÷ 6: yes (must be divisible by both 2 and 3) ÷ 7: no (remainder when divided by 7 is 4) ÷ 8: no (last three digits 236) ÷ 9: no (digit sum 12) ÷ 10: no (last digit 6)
Rules: 2, 5, 10 look at the last digit; 4 and 8 at the last two or three digits; 3 and 9 at the digit sum; 6 needs 2 and 3.
- 2Result
1236 is divisible by 2, 3, 4, 6.
How to use the divisibility rules calculator
- Type a whole number.
- Read the list of divisors from 2 to 10.
- Open the steps to see the rule behind each yes or no.
- Use the rules to simplify fractions quickly.
The rules
2: last digit even 3: digit sum divisible by 3 4: last two digits divisible by 4 5: ends in 0 or 5 6: divisible by 2 and 3 7: remainder test 8: last three digits divisible by 8 9: digit sum divisible by 9 10: ends in 0
The rule for 7 is shown as the exact remainder check.
Worked examples
Each example below is generated by the same calculator you used above, so the working always matches the answer.
1236
- Digit sum 12
Step-by-step working 2 steps
- 1Apply each divisibility rule
÷ 2: yes (last digit 6 is even) ÷ 3: yes (digit sum 12) ÷ 4: yes (last two digits 36) ÷ 5: no (last digit 6) ÷ 6: yes (must be divisible by both 2 and 3) ÷ 7: no (remainder when divided by 7 is 4) ÷ 8: no (last three digits 236) ÷ 9: no (digit sum 12) ÷ 10: no (last digit 6)
Rules: 2, 5, 10 look at the last digit; 4 and 8 at the last two or three digits; 3 and 9 at the digit sum; 6 needs 2 and 3.
- 2Result
1236 is divisible by 2, 3, 4, 6.
360
- Digit sum 9
Step-by-step working 2 steps
- 1Apply each divisibility rule
÷ 2: yes (last digit 0 is even) ÷ 3: yes (digit sum 9) ÷ 4: yes (last two digits 60) ÷ 5: yes (last digit 0) ÷ 6: yes (must be divisible by both 2 and 3) ÷ 7: no (remainder when divided by 7 is 3) ÷ 8: yes (last three digits 360) ÷ 9: yes (digit sum 9) ÷ 10: yes (last digit 0)
Rules: 2, 5, 10 look at the last digit; 4 and 8 at the last two or three digits; 3 and 9 at the digit sum; 6 needs 2 and 3.
- 2Result
360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10.
1001
- Digit sum 2
Step-by-step working 2 steps
- 1Apply each divisibility rule
÷ 2: no (last digit 1 is odd) ÷ 3: no (digit sum 2) ÷ 4: no (last two digits 1) ÷ 5: no (last digit 1) ÷ 6: no (must be divisible by both 2 and 3) ÷ 7: yes (remainder when divided by 7 is 0) ÷ 8: no (last three digits 1) ÷ 9: no (digit sum 2) ÷ 10: no (last digit 1)
Rules: 2, 5, 10 look at the last digit; 4 and 8 at the last two or three digits; 3 and 9 at the digit sum; 6 needs 2 and 3.
- 2Result
1001 is divisible by 7.
98765
- Digit sum 35
Step-by-step working 2 steps
- 1Apply each divisibility rule
÷ 2: no (last digit 5 is odd) ÷ 3: no (digit sum 35) ÷ 4: no (last two digits 65) ÷ 5: yes (last digit 5) ÷ 6: no (must be divisible by both 2 and 3) ÷ 7: no (remainder when divided by 7 is 2) ÷ 8: no (last three digits 765) ÷ 9: no (digit sum 35) ÷ 10: no (last digit 5)
Rules: 2, 5, 10 look at the last digit; 4 and 8 at the last two or three digits; 3 and 9 at the digit sum; 6 needs 2 and 3.
- 2Result
98765 is divisible by 5.
Common mistakes to avoid
Checking 6 with only one rule
A number needs both the 2-rule and the 3-rule to be divisible by 6.
Using the digit sum for 4
Divisibility by 4 depends on the last two digits, not the digit sum.
Misapplying the digit-sum rule for 9
The digit sum must itself be a multiple of 9, not just of 3.
Frequently asked questions
Why does the digit-sum rule work?
Because 10 leaves remainder 1 when divided by 3 or 9, so every power of ten does too, and a number has the same remainder as its digit sum.