Abelian group of order 155

Question

I am trying to prove that a group of order $155$ that is abelian must be cyclic, and since $155 = 5*31$, I think that the only choices are $\mathbb{Z}/155\mathbb{Z}$ and $\mathbb{Z}/31\mathbb{Z} \bigoplus \mathbb{Z}/5\mathbb{Z}$, which are isomorphic to each other by the fundamental theorem of abelian groups. However, I'm not quite sure why EVERY abelian group has to be isomorphic to a direct product of Z/nZ, or if that's even true.