Making a Factor Tree

Date: 03/26/98 at 17:49:27
From: Kelsy Snowman
Subject: making a factor tree

Dear Dr. Math,
  
How do you make a factor tree? I know what one is but my teacher gave 
us a quiz and I didn't know how to do it.

Kelsy Snowman

Date: 03/27/98 at 03:14:06
From: Doctor Mike
Subject: Re: making a factor tree

Dear Kelsy,

There are several ways to write these things down, and I will show you 
one. That will give you the idea. Here's an example.
   
Let's say you want to factor 630. Because there is a zero on the end
you know it has 10 as a factor. It can be written 63 * 10. Both of
these factors can be factored further. Ten is 5*2 and that's all.
63 is 9*7, which gives the prime 7 and also 9 which is 3*3.  We can
show all of this in a "tree" drawing like this.

                      630   
                     /   \
                    /     \
                   /       \
                 63         10  
                /  \        / \
               /    \      /   \  
              9      7    5     2   
             / \  
            /   \
           3     3   

All of the numbers at the bottom (the leaves on the tree) are prime
numbers, so you are done. To write out the factorization in an
equation, you multiply all of them like this: 630 = 3*3*7*5*2.  
Sometimes teachers want them written in increasing order like this:
630 = 2*3*3*5*7.
   
Sometimes people write the original number 630 on the bottom and 
have the connecting lines go upwards, so the "leaves" will be on top.
   
Whether you draw trees or not, the basic idea is that to factor a 
number completely, you first have to start somewhere, the way I 
started with 630 = 63*10. You could have started differently. You 
could have started by noticing that 630 is even and written down 
630 = 2*315. That's fine. No matter how you start, you have to keep on 
until everything is factored completely into primes.  
  
I hope this helps.   

-Doctor Mike,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/