Here is a great formula to calculate the factorial of ANY large number such as googol(10^100)!:
n!~Sqrt(π).n^n.e^-n.[8n^3 + 4n^2 + n + 1/30]^1/6
But, how do you use it when the display of most calculators can't go beyond 10^500? Ah, that is very good question! So, what to do? Of course, we take its Log base 10, term by term, and add them all up.
So, what is (10^100)! ?. Using the above formula and taking its Log, term by term, you get this Log of googo factorial:1 5657055180 9674817234 8871081083 3949177056 0299419633 3433885546 2168341353 5079112922 5270775050 6615682567.2120288667 3139448744 6086798636 1063111442 4189227464 7371063719 2096603409 4738605488 3374649052 4079270611..........to about 200 digits or so. Now, we discard the integer part of the Log and keep the decimal part. Then we raise this decimal part to base 10 and we get the first few-dozen or so digits of (10^100)!. And they are:
1 6294043324 5933737341 7934652983 5421728218 8842671486 6230362361 1936940922..etc.
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,
The value of 0! is 1, according to the convention for an empty product.[1]
The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence (i.e., permutations of the set of objects). This fact was known at least as early as the 12th century, to Indian scholars.[2] Fabian Stedman in 1677 described factorials as applied to change ringing.[3] After describing a recursive approach, Stedman gives a statement of a factorial (using the language of the original):
-Ally
