How to write $210\in\mathbb Z[\sqrt{-1}]$ as a product of prime elements?

Question

How can I write $210\in\mathbb Z[\sqrt{-1}]$ as a product of prime elements?

Progress

I factored $2\in\mathbb Z[i]=(1-i)(1+i)$ and $5\in\mathbb Z[i]=(2-i)(2+i)$. I cannot do it for $3$ and $7$ though.

Answer 1

If $p$ is a prime with $p \equiv 3 \bmod 4$, then $p$ is a prime element in $\mathbb{Z}[i]$. This is because $x^2+1$ is irreducible mod $p$.