The GCF of two numbers is 871.  Both of the numbers are even, neither
are multiples of the other.  What are the smallest two numbers these
could be?

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Request for Question Clarification by pinkfreud-ga on 31 Aug 2003 17:26 PDT

Are you certain you've stated this problem correctly?

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Clarification of Question by thomaspewter-ga on 31 Aug 2003 19:03 PDT

The question is typed exactly as it appears in a textbook?  I have
been working on this with my son for over a week and we cannot come up
with even numbers.

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Request for Question Clarification by directrix-ga on 31 Aug 2003 19:22 PDT

Someone made a newsgroup post asking the exact same question.

http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&th=387b50cd3fb24c3b&seekm=Vmhjr-5B29EF.15300225102000%40news.frii.com&frame=off

There is no answer. The reason is best summed up by the last post:

"There cannot be two such numbers, since if both are even so is the
GCF."

thomaspewter...

Perhaps I'm misunderstanding the question, but it seems to me
that, since the numbers must be even, that they must be 871
multiplied by an even number, and, since (871 x 2) will be
a common factor in other even multiples: (871 x 4) and (871 x 6),
then the smallest even numbers of which 871 is a *factor*, and
which are not a factor of each other, are (871 x 4) and (871 x 6).
Of course, 871 is not the GCF of these numbers, since (871 x 2)
holds that distinction.

sublime1-ga