Binomial Theorem/Factorial proof

Hi

Here's the question:

*There exists a positive integer *m *for which the coefficient of the middle term in the expansion of *(1+x)^(2m) *is odd. True or False?*

Our teacher solved it and I remember the answer is 'false', but I can't seem to remember how he did that. So basically we have to prove that (2m)!/(m! m!) can never be odd.

Sorry if the question is too elementary for this forum, or if this isn't the right place to post it.

(Btw, I'm new here. (Hi) And I'm 18. Sorry, I couldn't figure out how to properly use latex code. Is there a guide for it?)