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### What are the Factors of 33550336?

```
Date: 9 Apr 1995 01:09:17 -0400
From: Jirachai Chuchat
Subject: Re: Perfect Numbers

Do you know the factors for the Perfect Number,  33550336?  Thanks

Chris
```

```
Date: 9 Apr 1995 14:40:51 -0400
From: Dr. Ken
Subject: Re: Perfect Numbers

Hello there!

The perfect numbers that we know about, i.e. the even perfect numbers (we
don't know if any odd perfect numbers exist) are in the form

2^(n-1) * (2^n - 1).

It is known that whenever 2^n - 1 is prime (these primes are known as the
Mersenne primes), the number 2^(n-1) * (2^n - 1) is perfect.  In your case,
n=13, so the factorization is 33550336 = 2^12 * (2^13 - 1) = 2^12 * 8191,
and 8191 is prime.

Have fun with it!

-Ken "Dr." Math
```
Associated Topics:
College Number Theory

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