Divisibility rules/Rule for 5 and powers of 5 proof

A number $N$ is divisible by $5^n$ if the last $n$ digits are divisible by that power of 5.

Proof

An understanding of basic modular arithmetic is necessary for this proof.

Let the base-ten representation of $N$ be $a_ka_{k-1}\cdots a_1a_0$ where the $a_i$ are digits for each $i$ . Thus

$N = 10^k a_k + 10^{k-1} a_{k-1} + \cdots + 10 a_1 + a_0.$

Taking this $\mod 5^n$ we have

Thus if the last $n$ digits of $N$ are divisible by $5^n$ then $N$ is divisible by $5^n$ .