How to Find the Last Digit of a Power

Updated 4 October 2026

Last digits cycle every few powers — pin the exponent to the cycle.

Last digit of $7^{43}$7^43 = 3

How do you find the last digit of a power?

Last digits of powers repeat on a short cycle, so find the cycle, then reduce the exponent against its length. Powers of 7 end in 7, 9, 3, 1 and then start again, because only the last digit of each product matters: 9 × 7 = 63 ends in 3, and 3 × 7 = 21 ends in 1. The cycle is four long, so divide the exponent by 4. For 7^43, 43 leaves 3 when divided by 4, so 7^43 ends in the third digit of the cycle, which is 3. A remainder of 0 means the last digit of the cycle, so 7^40 ends in 1. The same steps work for any base, using only its last digit: 23^10 ends like 3^10, and powers of 3 end in 3, 9, 7, 1, so a remainder of 2 gives 9. The digits 0, 1, 5 and 6 never change, and 4 and 9 alternate every step, so their powers need no division at all.

1. Multiply by 7 and the last digit walks a ring: 7, 9, 3, 1, then 7 again.

2. The ring closes after 4 steps, so only 43 mod 4 = 3 decides where you land.

3. Ten whole laps land back at the start, and three more steps reach 3.

All 36 shortcuts: the Magic Tricks library.