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Q&A #5978


Prime factorization using trees

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From: Jeanne (for Teacher2Teacher Service)
Date: Mar 16, 2001 at 16:07:19
Subject: Re: Prime factorization using trees

Hi Helen,

I am not sure what you mean by "work a tree" but here is what I think
you mean.

Let's begin with a quick statement about prime numbers.

The number 2 is a prime number because it can only be expressed as
a product of 1 and itself.  The same can be said for 3, 5, 7, 11, 13 and so
forth.
(The number 8 is NOT a prime number because it can be expressed as 1 x 8 or
2 x 4.  It is a composite number.  The number 1 is neither prime nor
composite.)

Now for the "trees".  Rather than explain how to create them.  I thought I'd
give you some examples.

Here's a factor tree for the number 6.

           6
          / \
         2   3

(Note 2 x 3 = 6.  2 and 3 are factors of 6.)  We stop here because 2 and 3
are prime numbers.

There are several possible factor trees for the number 24.  They just depend
upon how your son chooses to break the numbers down.  The prime factorization
ends up being the same.

           24
           / \
          2  12   (12 isn't prime so we continue.)
             /\
            2  6    (6 isn't prime so we continue.)
              /\
              2 3

  So, 24 = 2 x 2 x 2 x 3.  (<--This is what I meant by the prime
factorization.)

Here's another for 24.
            24
            /\
           6  4   (Neither 6 nor 4 are prime so we continue.)
          /\  /\
         2 3  2 2

 So, 24 = 2 x 2 x 2 x 3

Factor trees have a way of "growing" and getting rather messy.  It is
important for your son to try and be as neat as possible in order to keep
track of the factors.

Hope this helps.
 -Jeanne, for the T2T service

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