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