Expert: Paul Klarreich - 3/10/2007

Question
Hi, I have a question on how to find out what 300! would equal out to and what an eaiser way would be to figure that out, becuase the way i was doing it would take forever.  I was doing 300*299*298.... but that will take way too long to come up with the answer

Answer
Questioner:   Mike
Category:  Calculus
 
Subject:  math
Question:  Hi, I have a question on how to find out what 300! would equal out to and what an eaiser way would be to figure that out, becuase the way i was doing it would take forever.  I was doing 300*299*298.... but that will take way too long to come up with the answer
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Hi, Mike,

My sentiments exactly. But if you want the exact answer, you don't have any choice.

HOWEVER, if you just want a reasonable approximation to 300!, there is  STIRLING'S APPROXIMATION, found in many references.  See, for example:

http://mathworld.wolfram.com/StirlingsApproximation.html
http://en.wikipedia.org/wiki/Stirling's_approximation
http://www.nist.gov/dads/HTML/stirlingappx.html

and you can use your calculator for the value without much difficulty.