NUMBER LOGIC / JD · 2026.10.19
Divisibility Rules for 2, 3, 5, 9 and 11
A compact reference with examples and checks.
Start with the last digit
A whole number is divisible by 2 when its last digit is even. It is divisible by 5 when its last digit is 0 or 5. Divisibility by 10 requires a final 0. These rules follow directly from base-ten place value.
Use the sum for 3 and 9
Add the decimal digits to test divisibility by 3 or 9. The number 4,536 has digit sum 18, so it is divisible by both. This shortcut tells you nothing directly about divisibility by 7.
The alternating test for 11
Alternately add and subtract digits. For 1,221, (1 − 2 + 2 − 1) = 0, which is divisible by 11. Consequently 1,221 itself is divisible by 11.
Combine tests carefully
Being divisible by 2 and by 3 guarantees divisibility by 6. Being divisible by 2 and 4 does not establish divisibility by 8. When unsure, use prime factors or direct division.