De Polignac's Formula/Examples/11 in 1000

Example of Use of Multiplicity of Prime Factor in Factorial
The prime factor $11$ appears in $1000!$ to the power of $98$.

That is:
 * $11^{98} \mathrel \backslash 1000!$

but:
 * $11^{99} \nmid 1000!$

Proof
Let $\mu$ denote the power of $11$ which divides $1000!$