De Polignac's Formula/Examples/5 in 1000

Example of Use of Multiplicity of Prime Factor in Factorial
The prime factor $5$ appears in $1000!$ to the power of $249$.

That is:
 * $5^{249} \mathrel \backslash 1000!$

but:
 * $5^{250} \nmid 1000!$

Proof
Let $\mu$ denote the power of $5$ which divides $1000!$