What is the total number of zeroes in $n!$?
I do not want to know the number of trailing zeroes in $n!$.
Let us take an example to understand what I want to know.
$7! = 5040$. The number of trailing zero in $7!$ is $1$. But the total number of zeroes in $7!$ is $2$.
I would like to know if there is any formula that gives me directly the total number of zeros in $n!$.
Can you help me derive one?