# A googolplex expressed in factorial form?

1. Feb 6, 2016

### Saracen Rue

Does anybody know what the factorial form of a googolplex would be?

2. Feb 6, 2016

### Mentallic

So you're asking to calculate the inverse gamma function, since the gamma function and the factorial are closely related. i.e. you want to solve for n in
$$n!=10^{10^{100}}$$

I can give you a quick start on the approximate magnitude of n. Since a crude approximation is $n!\approx n^n$, then choosing $n=10^{100}$ gives us
$$n^n=\left(10^{100}\right)^{\left(10^{100}\right)}=10^{100\times 10^{100}}=10^{10^{102}}\approx 10^{10^{100}}$$

hence n is somewhere in the ballpark of a googol.

Unless of course, you meant something else by your OP. Maybe you were asking what $$10^{10^{100}}!$$ is?

3. Feb 6, 2016

### Saracen Rue

Yes I was asking what 'n' would have been, and thank you for helping.

4. Feb 6, 2016

### Bill_Nye_Fan

I tried to get Wolfram Alpha to solve but it exceeded the standard calculation time - maybe someone with a pro account can try it.

Anyway just through guessing I managed to get 102483838377090000000000000000000000000000000000000000000000000000000000000000000000000000000000000! (1.0248383837709e+98!) as an answer.

Last edited: Feb 6, 2016