Question

How do you write `60` using factorials?

Answer 1

`(5!)/(2!)`

Explanation:

First, try to find a series of consecutive integers whose product is `60`.

`60=2^2xx3xx5=5xx4xx3`

Note that `5xx4xx3` is the start of the `5!` factorial chain, without `2! =2xx1`.

`60=5xx4xx3=(5xx4xx3xx2xx1)/(2xx1)=(5!)/(2!)`

This is the simplest way to express `60`, but we can try in more exotic ways:

`60=10xx6=(10!)/(9!)xx(6!)/(5!)=((10!)(6!))/((9!)(5!))`