How do you write $60$ using factorials?

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Answer 1 · 2016-02-03T16:09:54

$(5!)/(2!)$

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:

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

How do you write 6060 using factorials?