Find the unit digit of $7^{2026}$.

Find the unit digit of $7^{2026}$.
  1. $1$
  2. $3$
  3. $7$
  4. $9$

Solution

Unit digits of $7^{1}, 7^{2}, 7^{3}, 7^{4}$ are $7, 9, 3, 1$, then the cycle repeats with period 4. Since $2026 = 4 \times 506 + 2$, the unit digit equals that of $7^{2} = 49$, i.e., $9$.

Asked in: IMO

Practice more EXPONENTS AND POWERS questions on Aicharya