How to Find the Prime Factorization of a Whole Number

Date: 11/29/2005 at 20:31:03
From: Tanner
Subject: I still don't get prime factorization!

My teacher told me how to do prime factorization, plus I read YOUR 
definition about it, but I still don't get it!  Please help!  I know
how to do the first multiple but then after that I get confused.

Date: 11/29/2005 at 23:40:34
From: Doctor Ian
Subject: Re: I still don't get prime factorization!

Hi Tanner,

Once you find the first multiple, you're just doing the same problem
with another number. 

For example, suppose I'm trying to find the prime factorization of 56.
I know it's divisible by 2.  So 

  56 = 2 * 28

But this also means

  56 = 2 * (prime factorization of 28)

So now I can forget about that, and work on 28.  It's even, so it's
divisible by 2:

  28 = 2 * 14

     = 2 * (prime factorization of 14)

Again, I can forget about everything except this last number.  14 is
divisible by 2, so I have


  14 = 2 * 7

     = 2 * (prime factorization of 7)

But 7 is prime!  So we've bottomed out.  Now let's go back to the
beginning:

  56 = 2 * (prime factorization of 28)

     = 2 * 2 * (prime factorization of 14)

     = 2 * 2 * 2 * (prime factorization of 7)

     = 2 * 2 * 2 * 7

Does this make sense? 

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

Date: 12/02/2005 at 21:41:49
From: Tanner
Subject: Thank you (I still don't get prime factorization!)

Thank you so much for answering my question!  Because of your 
helpfulness I passed that kind of question on my test!!

- Tanner