Factorial of a factorial over a factorial

Number Theory Level 2

Solve for $x$ .

$\large \frac{(6!)!}{6!}= \ x!$

2 solutions

Chew-Seong Cheong
Jun 27, 2019

$\dfrac {(6!)!}{6!} = \dfrac {720!}{720} = 719!$ . Therefore, $x=\boxed{719}$ .

Minor typo in the denominator........it should be $6!$ instead of $61$

Aaghaz Mahajan - 1 year, 11 months ago

Thanks. I forgot the shift key.

Chew-Seong Cheong - 1 year, 11 months ago

I solved like this too.

Marc Tudosoiu - 1 year, 11 months ago

Chris Lewis
Jun 27, 2019

In general, $\frac{n!}{n}=(n-1)!$ . In this case we have $n=6!=720$ , so $x=720-1=\boxed{719}$ .