Prove that a factor group of an Abelian group is Abelian.

I'm a bit confused by the whole factor group affair, now I assume G is an Abelian group, and suppose that H is a factor group of G.

Then does that mean H is a normal subgroup of G such that G|H is a group?

By a theorem, I know that G|H is a group under the operation (aH)(bH)=abH. Now, is this the right theorem for to use to solve this problem?

Thanks.