The unit's digit in $13^{61}$ is

3

The correct answer is Option (2) → 3 **

Unit digit of $13^{61}$ depends on unit digit of 3.

Powers of 3 (unit digits):

$3^1 \rightarrow 3$

$3^2 \rightarrow 9$

$3^3 \rightarrow 7$

$3^4 \rightarrow 1$

Cycle length = 4

Compute: $61 \mod 4$:

$61 \mod 4 = 1$

So unit digit = unit digit of $3^1 = 3$

The unit digit of $13^{61}$ is 3.