Explaining Greatest Common Factor

Date: 12/19/2005 at 21:12:30
From: Trinity 
Subject: I do not understand what GCF is

Dr. Math,

I am trying to understand what GCF is but I just can not get it.  It
is so hard to understand.  I think it has something to do with
multiplication.  Please help me. 

Date: 12/19/2005 at 22:40:45
From: Doctor Ian
Subject: Re: I do not understand what GCF is

Hi Trinity,

Often when they make up a name like "greatest common factor", you can
figure out what it means just by looking at the individual words. 

For example, let's look at two numbers, like 12 and 20.  What are the
factors of 12?  Those are the numbers that evenly divide it:

  12 = 1 * 12
     = 2 *  6
     = 3 *  4          Factors: 1, 2, 3, 4, 6, 12

What about the factors of 20?

  20 = 1 * 20
     = 2 * 10
     = 4 *  5          Factors: 1, 2, 4, 5, 10, 20

Do they have any factors in common?  That is, are there any numbers
that are factors of both, numbers that appear in both lists?  In fact,
there are:

  1, 2, 4

So these are "common factors" of 12 and 20.  So far, so good?

Now, of these three common factors, which is the greatest?  That would
be 4, right?  So 4 is the "greatest common factor" of 12 and 20.

Does that make sense?

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

Date: 12/21/2005 at 08:09:22
From: Trinity 
Subject: Thank you (I do not understand what GCF is)

Thank you so much.  I understand it now!