I know that an ideal P in $\mathbb{Z}\_n$ is prime if and only if $\mathbb{Z}\_n/P$ is an integral domain and an ideal m in $\mathbb{Z}\_n$ is maximal if and only if $\mathbb{Z}\_n$/m is a field. 
I think I've figured out that $\mathbb{Z}\_p$ where p is a prime that divides n make up the maximal ideals.

I have no idea how to figure out which are prime. Help?