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### Greatest Common Factor

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Date: 06/02/99 at 23:18:13
From: christopher west
Subject: Greatest common factor

The GCF of two numbers is 479. One number is even, and the other
number is odd. One number is NOT a multiple of the other. What are
the smallest numbers these could be?

I have used calculator, paper and pencil, and mental math, and still
cannot figure it out.
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Date: 06/03/99 at 08:35:41
From: Doctor Peterson
Subject: Re: Greatest common factor

Hi, Christopher.

Let's take a simpler problem, and see what reasoning we can use:

The GCF of two numbers is 7. One number is even, and the other
number is odd. One number is NOT a multiple of the other. What are
the smallest numbers these could be?

What we're told is that the two numbers A and B have these properties:

The GCF of A and B is 7.
A is even (so it is a multiple of 2 as well as of 7).
B is odd (so it is not a multiple of 2).
A is not a multiple of B and B is not a multiple of A.

(This last statement could be a misinterpretation; a popular trick
question involves the statement that "one of the two coins is not a
nickel," and the solution requires taking this to mean that one is
not, but the other IS a nickel. I'm assuming this is not a trick
question where B is not a multiple of A, but A IS a multiple of B.)

We have to start with 7 and multiply it by different things to get A
and B. We know we want to multiply by 2 to get A:

A = 7 * 2 * ?
B = 7 * ?

If we just stopped there with A = 14 and B = 7, one would be a
multiple of the other. So we'll have to multiply B by something other
than 2, so it won't divide A evenly. What's the smallest number that
could be?

Now try doing the same thing with your original problem.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Middle School Factoring Numbers

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