I can only thin of a hot and miss method to do this . That is using Stirlings approximation for n!-
ln n! = approx n ln n - n
so if we try n = 60 this gives 4.2796 * 10^80
so we could try higher values:-
n = 65 gives an 89 digit number
n = 70 gives 98 digit number
n=71 gives me an memory error on my calculator!
Lets try an online calculator
Web2.0 calculator gives a 101 digit number or n=71
70 is your answer
