The number 6¹², when divided by 13 given remainder:

1

The correct answer is Option (1) → 1

$6^1(\text{mod 13})=6$

$6^2=6×6=36⇒36÷13=2$ remainder 10

So,

$6^2(\text{mod 13})=10$

$6^3(\text{mod 13})=8$

$6^4(\text{mod 13})=9$

$6^5(\text{mod 13})=2$

$6^6(\text{mod 13})=12$

$6^7(\text{mod 13})=7$

$6^8(\text{mod 13})=3$

$6^{13}(\text{mod 13})=1$