Suppose that $\langle k \rangle$ and $\langle n \rangle$ are cyclic subgroups of $\mathbb{Z}$ (the integers).
Prove that $\langle k\rangle \big/ \langle n \rangle$ is isomorphic to $\mathbb{Z}_{(n/k)}$.
I am having trouble even starting this. The solution says that if $k$ divides $n$, then $\langle k\rangle \big/ \langle n \rangle$ is a cyclic group of order $n/k$. So it is isomorphic to $\mathbb{Z}_{(n/k)}$. How is this true?