The unit's digit in $13^{61}$ is
Answer & explanation
Correct answer: option 2
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.