Elementary methods in number theory Theorem 1.12 $v_p(n!)=\sum_{r=1}^{[\log_p n]}[\frac{n}{p^r}]$

For every positive integer $n$ and prime $p$,
\begin{equation}
v_p(n!)=\sum_{r=1}^{[\log_p n]}[\frac{n}{p^r}]
\end{equation}

This formula is obvious(Why?).