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Divisibility rules 2 through 11

Number system questions — factors, HCF/LCM, simplification — move much faster when you can check divisibility by sight instead of doing the actual division.

2, 5, 10 — check the last digit

Divisible by 2: last digit is even (0, 2, 4, 6, 8).

Divisible by 5: last digit is 0 or 5.

Divisible by 10: last digit is 0.

3 and 9 — sum the digits

Divisible by 3: add up all the digits — if that sum is divisible by 3, so is the original number.

Divisible by 9: same idea, but the digit sum needs to be divisible by 9.

Example: 4,572 — digits sum to 4+5+7+2 = 18. 18 is divisible by both 3 and 9, so 4,572 is divisible by both.

4 and 8 — check the last few digits

Divisible by 4: the last two digits, read as their own number, are divisible by 4.

Divisible by 8: the last three digits, read as their own number, are divisible by 8.

Example: 71,928 — last two digits "28" are divisible by 4, so 71,928 is divisible by 4. Last three digits "928" ÷ 8 = 116, so it's divisible by 8 too.

6 — combine two rules

Divisible by 6: the number must pass both the rule for 2 (even) and the rule for 3 (digit sum divisible by 3) at the same time.

11 — alternating sum

Divisible by 11: add the digits in the odd positions, add the digits in the even positions, and subtract. If the result is 0 or a multiple of 11, the number is divisible by 11.

Example: 9,152 — odd positions (from the right): 2 and 1 → sum 3. Even positions: 5 and 9 → sum 14. Difference: 14 − 3 = 11. That's a multiple of 11, so 9,152 is divisible by 11.

7 — the one without a clean shortcut

There's a rule for 7 (double the last digit, subtract it from the rest, repeat), but it's slow enough that for most exam purposes, direct division or estimation is just as fast. Worth knowing it exists, not worth memorizing as a speed method.

Practice it

Practice arithmetic → · See the rest of the shortcuts guide →