# De Polignac's Formula/Examples/11 in 1000

## Example of Use of De Polignac's Formula

The prime factor $11$ appears in $1000!$ to the power of $98$.

That is:

$11^{98} \divides 1000!$

but:

$11^{99} \nmid 1000!$

## Proof

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

 $\ds \mu$ $=$ $\ds \sum_{k \mathop > 0} \floor {\frac {1000} {11^k} }$ De Polignac's Formula $\ds$ $=$ $\ds \floor {\frac {1000} {11} } + \floor {\frac {1000} {121} }$ $\ds$ $=$ $\ds 90 + 8$ $\ds$ $=$ $\ds 98$

$\blacksquare$