I am having troubles with this deceptively simple problem:

Show that for any integer n that $\displaystyle \frac{1}{n}$ will be a terminating sexagesimal iff n's prime factors only consist of 2,3 and 5.

In other words $\displaystyle \frac{1}{n}$ will terminate in base 60 iff $\displaystyle n = 2^a*3^b*5^c$