Disjoint cycles

Question

Suppose I am given an element $f$ in $S_7$, so that $f=(4,1,5)(3,2)(1,5,3)$.

I want to write this as a product of disjoint cycles.

How would I do this?

Answer 1

Do the product in cycles (when you're done with one cycle beginning with the next smaller number not in the cycle already written down):

$$f=(1\;4)(2\;3\;5)$$