Define thenormN($\displaystyle \alpha$)for an element $\displaystyle \alpha= a + b\sqrt{-5} in Z\sqrt{-5} $. Show that any common divisor of $\displaystyle 1 + \sqrt{-5}$ and 2 in the ring $\displaystyle Z\sqrt{-5}$ is a unit.

I know that

N($\displaystyle 1 + \sqrt{-5})= 6$ and that

N(2)= 4

But how do you show that any common divisor is in the ring?