Find the remainder when 32013 is divided by 13.
| Number | Remainder when divided by 13 |
| 31 | 3 |
| 32 | 9 |
| 33 | 1 |
| 34 | 3 |
| 35 | 9 |
| 36 | 1 |
| 37 | 3 |
| 38 | 9 |
| 39 | 1 |
| . | . |
| . | . |
| . | . |
| 32013 | ? |
When successive powers of 3 are divided by 13, a pattern emerges. Since 2013 is a multiple of 3, the remainder when 32013 is divided by 13 is 1.
(Note: You can adapt this to any power of 3 your students might like.)