Divisibility Rules Table
A divisibility rule is a shortcut for checking whether a number divides another evenly, without doing the full division. This reference table covers the rules for 2 through 12 with worked examples, plus a checker for any number.
Divisibility Checker
Enter a whole number to see which numbers from 2 to 12 divide it evenly.
÷ 2Yes
÷ 3Yes
÷ 4Yes
÷ 5Yes
÷ 6Yes
÷ 7No
÷ 8Yes
÷ 9Yes
÷ 10Yes
÷ 11No
÷ 12Yes
Divisibility Rules (2–12)
| Divisor | Rule | Example |
|---|---|---|
| 2 | The last digit is even (0, 2, 4, 6, 8). | 348 — last digit 8 is even ✓ |
| 3 | The sum of the digits is divisible by 3. | 234 — 2+3+4=9 (÷3) ✓ |
| 4 | The last two digits form a number divisible by 4. | 316 — 16 ÷ 4 = 4 ✓ |
| 5 | The last digit is 0 or 5. | 265 — ends in 5 ✓ |
| 6 | The number is divisible by both 2 and 3. | 318 — even, and 3+1+8=12 (÷3) ✓ |
| 7 | Double the last digit and subtract it from the rest; if the result is divisible by 7 (or 0), so is the original. | 203 — 20 − (2×3) = 14 = 7×2 ✓ |
| 8 | The last three digits form a number divisible by 8. | 1,624 — 624 ÷ 8 = 78 ✓ |
| 9 | The sum of the digits is divisible by 9. | 486 — 4+8+6=18 (÷9) ✓ |
| 10 | The last digit is 0. | 790 — ends in 0 ✓ |
| 11 | The alternating sum of the digits (add, subtract, add, …) is divisible by 11 (or 0). | 2,728 — 8−2+7−2=11 ✓ |
| 12 | The number is divisible by both 3 and 4. | 156 — 1+5+6=12 (÷3), and 56 ÷ 4 = 14 ✓ |
Why These Rules Work
Most digit-sum rules (3, 9) work because 10 ≡ 1 (mod 3) and 10 ≡ 1 (mod 9), so each digit contributes its own value to the remainder regardless of position. The last-digits rules (2, 4, 5, 8, 10) work because 10, 100, and 1,000 are themselves divisible by 2, 4, 5, 8, and 10 — so only the trailing digits affect the remainder. Composite divisors like 6 and 12 simply combine the rules for their prime factors.