Let $K$ be an algebraic number field. Let $I$ be an integral ideal of $O_K$ such that $pq \mid N(I)$, where $p$ and $q$ are distinct primes. Prove that $I$ is not a prime ideal.
I am unsure of how to complete this problem. I let $N(I) = pqr$. Hence we have that $<N(I)> = <pqr>$ and we also have that $I \mid N(I) = <pqr>$ but I am not sure what to do after this. I also don't see any way that I can use the property $N(AB) = N(A)N(B)$ because I am doing a proof by contradiction and assuming that $I$ is prime. Could someone please help me with this problem?