Quiz Entry - updated: 2026.07.14
Give a fast decision list: which rule for which divisor?
Last-digits for the 2-family, digit-sum for 3 and 9, alternating sum for 11, and combine for composites.
| Divisor | Test |
|---|---|
| 2, 5, 10 | last digit |
| 4 / 8 | last two / three digits |
| 3 / 9 | digit sum ÷ 3 / ÷ 9 |
| 6 | ÷2 and ÷3 |
| 11 | alternating digit sum ÷ 11 |
| 7 | subtract 2× last digit (repeat), or the 1001 block method |
| 7, 11, 13 | 3-digit block alternating sum |
Composites (6, 12, 15, 45…) reduce to testing their coprime prime-power factors separately.