Unit Digit of Large Powers
Find the last digit of a huge power quickly.
Unit digits repeat in a cycle of 4 — use power ÷ 4 remainder.
1How it works
The unit digit of a number raised to a power repeats in a short cycle (length 1, 2 or 4). Divide the exponent by 4 and use the remainder to pick the right digit.
2How to apply (in seconds)
- Note the unit digit of the base.
- Divide the power by 4 and find the remainder.
- Use the remainder to read the repeating unit digit (remainder 0 → take the 4th in the cycle).
3Worked examples
Example 1 Worked solution
Q. Find the unit digit of 7¹⁰².
- Unit digits of 7: 7, 9, 3, 1 (cycle of 4).
- 102 ÷ 4 leaves remainder 2.
- The 2nd digit in the cycle is 9.
✓ 9
4When to use it
- ✦Unit-digit and remainder MCQs.
5Cautions & tips
- !Digits 0, 1, 5 and 6 always keep the same unit digit.
- !Remainder 0 means take the last digit of the cycle.