Odd Factorial

Date: 12/24/2001 at 01:14:13
From: Shridhar
Subject: Factorial

Can a factorial ever be odd? If so, then is 'n' odd in that case?

Date: 12/24/2001 at 13:11:50
From: Doctor Jaffee
Subject: Re: Factorial

Hi Shridhar,

1! (one factorial) is equal to 1, which is odd; also, 0! = 1. 

But if n is greater than 1, then n! = n(n - 1)(n - 2)(n - 3)*...3*2*1 
and since 2 is a factor of n! when n is greater than 1, n! must be 
even.

I hope this helps. Thanks for writing to Ask Dr. Math and let me know 
if you want to discuss this problem some more. 

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/