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?

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- Oct 2nd 2007, 06:01 PMtttcomraderOrder of a factor group
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? - Oct 2nd 2007, 06:12 PMThePerfectHacker
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 $\displaystyle |G|/|H|$.