What is the remainder when $7^{100}$ is divided by 5?

Explanation

1. 01

   $7 \equiv 2 \pmod{5}$, and $2^{4} = 16 \equiv 1 \pmod{5}$.

2. 02

   $7^{100} \equiv 2^{100} = (2^{4})^{25} \equiv 1$.