Q&A #6030

GCF & LCM factor trees

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From: Jeanne (for Teacher2Teacher Service)
Date: Mar 27, 2001 at 21:23:52
Subject: Re: GCF & LCM factor trees

Hi Jennifer,

A factor tree is a way of breaking down a number.  There are other ways of
accomplishing this task.  It really isn't the tree itself that is so
important in mathematics.  It is the act of factoring that is the important

Not long ago we were working on square roots in my basic Algebra 1 class and
they had to make sure their answer was in "simplest radical form."  For
example,  they had to change the "square root of 24" to "2 times the square
root of 6."

       sqr(24) = sqr(4*6) = sqr(4) * sqr(6) = 2*sqr(6)

It was very helpful that all of my students knew how to factor 24 to 4*6.
In fact most of them used a factor tree.

In higher level classes, factoring is one of many tools we use to help us
solve polynomial equations, to find the x-intercepts of polynomial
functions, to find the location(s) of vertical asymptotes and more.

The topic you listed for your question mentioned GCF and LCM. Here is copy
of part of my response to a teacher asking about these topics.  I am
including in my response to you so that you can see another way of finding
GCF and LCM.

"...I also wanted to let you know that I can remember the frustration of
teaching these concepts to students in my general math classes. Yes, the
students did have troubles.  My experience was that they had more trouble
when I taught methods of finding them separately than when I taught a single
method together.

Here's what I mean by teaching them together.

The greatest common factor and least common multiple can be found using a
graphic organizer which is a division method.  I am not sure if this is what
you already do, but here goes.

Suppose we want to find the GCF of 12 and 18.  Set up the upside down
division symbol as follows:


"What factor (it doesn't have to be prime) is common to both?"  "2"

        6      9

"What factor is common to both 6 and 9?"  "3"

        2      3

"What factor is common to both 2 and 3?"  "1"

        2      3

Conclusion 1:  GCF of 12 and 18 is 2*3 or 6.

Conclusion 2:  LCM of 12 and 18 is 2*3*1*2*3 or 36.

My kids really like this way of keeping things organized!  These
don't "grow" uncontrollably like factor trees do and they don't seem to lose
factors as much."

Hope this helps.

-Jeanne, for the T2T service

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