Divisibility Rules — 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
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1. Divisibility Rule for 2
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
Examples: 134 ✓ (ends in 4) | 571 ✗ (ends in 1)
2. Divisibility Rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 126 → 1+2+6 = 9. 9 is divisible by 3 ✓. So 126 ÷ 3 = 42.
Example: 457 → 4+5+7 = 16. 16 is not divisible by 3 ✗.
3. Divisibility Rule for 4
A number is divisible by 4 if its last two digits form a number divisible by 4.
Example: 1,736 → last two digits = 36. 36 ÷ 4 = 9 ✓.
4. Divisibility Rule for 5
A number is divisible by 5 if its last digit is 0 or 5.
Examples: 320 ✓ | 745 ✓ | 672 ✗
5. Divisibility Rule for 6
A number is divisible by 6 if it is divisible by both 2 AND 3.
Example: 312 → Ends in 2 (divisible by 2 ✓) | 3+1+2=6 (divisible by 3 ✓) → Divisible by 6 ✓
6. Divisibility Rule for 7
Double the last digit and subtract it from the rest. If the result is divisible by 7, so is the original number.
Example: 203 → 20 − (2×3) = 20 − 6 = 14. 14 ÷ 7 = 2 ✓. So 203 is divisible by 7.
7. Divisibility Rules for 8, 9, 10, 11
- Rule for 8: Last three digits divisible by 8. Example: 1,720 → 720 ÷ 8 = 90 ✓
- Rule for 9: Sum of digits divisible by 9. Example: 729 → 7+2+9 = 18 ÷ 9 = 2 ✓
- Rule for 10: Last digit is 0. Example: 950 ✓
- Rule for 11: Alternating sum of digits is divisible by 11. Example: 1,331 → (1+3) − (3+1) = 4−4 = 0 ✓ (0 is divisible by 11)