What is the fastest way to compute 285714! (I.e. the factorial of 285714)? Note: Approximate values?

Answer 1

find a computer program capable of it, and have a go of it like that. factorials are annoying to compute.

Answer 2

Sterling's approximation says it is approximately:

[(2*pi*285714)^(1/2)]*
[(285714/e)^285714]

so to get a very good estimate of the number of digits, take the log base 10 of the above and use the rule that log(a^b) = b*log(a). More specifically, the log of the above equation would be:
(1/2)log(2*pi*285714) + 285714*log(285714/e), so this would be approximately the number of digits of 285714!

Hey that's an answer with both an e and a pi -- you gotta like that!

(Of course a crude approximation of the number of digits is 6*285714, since each number in the product is less than 1000000).

Answer 3

use Stirling's formula

n! = sqrt(2 pi *n) * n^n / e^n ((approx))