From: Suzanne A. 
To: Teacher2Teacher Public Discussion
Date: 2000062816:46:28
Subject: Re: HELP... Greatest Common Factors

Well, I guess it would be helpful to start by thinking about what a
GCF is. GCF stands for Greatest Common Factor and if 850 is the GCF of
two numbers then that means that 850 is the largest number that will
divide into both numbers evenly.

So, I would start by listing some possible numbers that 850 will
divide into. That would include:

850  (850 X 1)
1700 (850 X 2)
2550 (850 X 3)
3400 (850 X 4)
and so on.....

Now, let's consider the second condition. "Neither number is divisible
by the other. If we answered that the two numbers were 850 and 1700,
you might agree that 850 divides into 1700 exactly two times. Also, if
you consider 1700 and 3400 we again find that 1700 divides into 3400
exactly two times.

What about 1700 and 2550? 1700 doesn't divide evenly into 2550! So, I
think we found the two smallest numbers that fit all of the
conditions.

In general to decide the answer, I would start by listing the
multiples of the GCF (the number times 1, the number times 2, the
number times 3, etc.) and then consider the other conditions to decide
which numbers would satisfy all of the conditions.

I hope that helps.

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