I need to show that if $$f: \mathbb Z_{15} \to \mathbb Z_8$$ then $f \equiv 0$
I have found that the number of homomorphisms between $\mathbb Z_n$ and $\mathbb Z_m$ is the $\gcd(n,m)$
Thus the $\gcd(15,8)=1$ meaning that the trivial homomorphism is the only homomorphism.
How can I show that the number of homomorphisms between $\mathbb Z_n$ and $\mathbb Z_m$ is indeed $\gcd(n,m)$?