Divisibility Test Calculator
Become a master of testing for divisibility with the help of our divisibility test calculator!
Divisible by2, 3, 4, 6, 8, 9, 12
Digit sum18
Digital root9
Prime factorisation2^3 × 3^3 × 17
The tests
| Divisor | Divides? | Test |
|---|---|---|
| 2 | Yes | last digit is even |
| 3 | Yes | digit sum 18 is divisible by 3 |
| 4 | Yes | last two digits (72) divide by 4 |
| 5 | No | last digit is 0 or 5 |
| 6 | Yes | divisible by both 2 and 3 |
| 8 | Yes | last three digits (672) divide by 8 |
| 9 | Yes | digit sum 18 is divisible by 9 |
| 10 | No | last digit is 0 |
| 11 | No | alternating digit sum divides by 11 |
| 12 | Yes | divisible by both 3 and 4 |
The method
digit-based tests for the small divisors
Why the digit-sum tests work
10 leaves remainder 1 when divided by 9, so every power of 10 does too. That means a number and its digit sum leave the same remainder mod 9 — and hence mod 3. It is the same reason the alternating digit sum works for 11: there, 10 leaves remainder −1, so the powers alternate in sign.