number theory - Dividing $2012!$ by $2013^n$

What's the largest power $n$ such that $2012!$ is divisible by $2013^n$?

It doesn't look like its divisible at all since $2012<2013$; am I right?

Answer

$2013=3 \times 11 \times 61$. Thirty-two naturals $\leq 2012$ are divisible by $61$ and none are divisible by $61^2$. At least thirty-two naturals are divisible by $11$ and by $3$, and so we have that $2013^{32}$ divides $2012!$ but no larger power of $2013$ does.