I Identify Factorial: Is It Possible?

[DuckAmuck]

Is there a way to identify a factorial without referring to computation of a factorial?

For example, is there a way to identify 5040 as a factorial and a way to identify 5050 as not a factorial?

 

[chiro]

Hey DuckAmuck.

The best thing I could advise is equating a value to the Gamma function (which generalized the factorial) and see if you get an integer value.

https://en.wikipedia.org/wiki/Gamma_function

 

[micromass]

You can check divisibility by $2$, $3$, etc. That is often very easy to do.

Also, check Wilson's theorem.