Divisibility Rule for 11
✅ Shortcut: Find the alternating sum of the digits. If the result is divisible by 11 (or equals 0), then the number is divisible by 11.
Steps:
- Take the digits of the number.
- Alternately add and subtract them.
- If the result is divisible by 11 or is 0, it’s divisible by 11.
Examples:
| Number | Alternating Sum | Result | Divisible by 11? |
|---|---|---|---|
| 2728 | 2 − 7 + 2 − 8 | -11 | ✅ Yes |
| 121 | 1 − 2 + 1 | 0 | ✅ Yes |
| 1234 | 1 − 2 + 3 − 4 | -2 | ❌ No |
| 462 | 4 − 6 + 2 | 0 | ✅ Yes |
| 713 | 7 − 1 + 3 | 9 | ❌ No |