# Math Help - Order of a factor group

1. ## Order of a factor group

Find the order of $Z_{60}/<15>$

Now <15> = {0, 15, 30, 45}, from a similar problem that I have done before, I think the answer would be 15, is that right?

Find the order of $Z_{60}/<15>$
Let $G$ be a finite group and $H$ be a normal subgroup. Then $G/H$ is the set of all co-sets of $H$ forming a group (called factor group). By Lagrange's theorem the number of cosests (denoted by $(G:H)$) of $H$ under $G$ is $|G|/|H|$.