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Q&A #6030

Teachers' Lounge Discussion: GCF & LCM factor trees

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2002092605:30:22
Subject: Re: Math; What are factor trees?

What are factor trees?


Factor trees are a way to express a composite number as a product of
primes.

For example, lets factor 72:

                           72

                         /    \
                        8      9   
                       / \    / \
                      2   4  3   3
                         / \
                        2   2

Thus, 72 = 2 x 2 x 2 x 3 x 3.  If the above stays in alignment, then
that's it.

I usually have algebra students write in a column form when trying to
find factors of numbers such as 180:

1 x 180
2 x  90  (double first one and take half of the other factor)
3 x  60  ( triple first one and take 1/3 of the other factor)
4 x 45   (double 2nd one and take half of the other factor)
5 x 36
6 x 30
9 x 20
10 x 18
12 x 15 ( double the 6th one and half the other factor) 

That should do it since the next one will be 15 x 12.  Thus, I use
doubles and halves, triples and thirds, etc.

The column method is not necessarly for finding a product of primes,
but for factoring trinomial expressions in algebra of the form:
ax^2 + bx + c.  

Of course, you may prefer to list the factors horizontial vice
vertical.  

Someone expressed dissatisfaction with factor trees.  They are are
often a good way to factor.  I don't believe there is a best way that
everybody should teach.  There is always more than one way to do
something.

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