Expert: Abe Mantell - 8/27/2010

Question
How can v faid 100! value without multiplying all the numbers individually...
is there any shortcut to find n! for large numbers...

Answer
I think you meant to ask "How can WE FIND 100! without multiplying all the numbers out?"  Yes?

We could add log(100) + log(99) + log(98) + ... + log(2) + log(1)
in base 10...then take that result and raise 10 to that power
(or any base will be OK, but base 10 is nice because the sum will
give us the order of magnitude).  It would give about 157.9700037.
Thus, 100! is about 10^157.9700037 = 10^0.9700037 x 10^157
which is about 9.33262 x 10^157.

Otherwise, we could use Stirling's apprximation:
n! is approximately sqrt(2*pi*n)*(n/e)^n
where sqrt means the square root and e=2.718281828...

If case you are curious:
100! is exactly
=93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
or about 9.332621544 x 10^157, and Stirling's approximation
gives about 9.324847782 x 10^157

Abe