Q:

Large Factorial Divisibility

I need some help regarding factorials.  Say I have a number like $2012!$. I want to test whether it is divisible by $100$. How would I do this?  I already know how to use Stirling's approximation, but want to know if there is an even better way. 

A:

If you were to write out $2012!$ it would look something like this:
$$2012!=1\times2\times3\times4\times\cdots\times99\times100\times101\times\cdots\times2011\times2012$$
Note that is is multiplied by 100 (and lots of other numbers) so it is divisible by 100.