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### 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/
```
Associated Topics:
Middle School Factorials

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