Question

What is remainder $4^{96}÷6$

Answer 1

If we take $4^1$ divided by $6$, the remainder is $4.$

$4^2$ divided by $6$, remainder is $4.$

$4^3$ divided by $6$, remainder is $0$

$4^4$ divided by $6$, remainder is $4$

and so on...

So, When $4$ has even a number of powers, it will always give remainder $4$ on dividing by $6.$

The remainder of $4^{96}÷6$ is $4$.