The non-negative remainder when $7^{30}$ is divided by 5 is

4

The correct answer is Option (2) → 4

Find $7^{30} \bmod 5$.

$7 \equiv 2 \pmod{5}$

So $7^{30}\equiv 2^{30} \pmod{5}$.

Powers of $2$ modulo $5$ repeat every $4$:

$2^{1}\equiv2$

$2^{2}\equiv4$

$2^{3}\equiv3$

$2^{4}\equiv1$

$30 \bmod 4=2$

$2^{30}\equiv2^{2}\equiv4\pmod{5}$

final answer: $4$