Originally posted by Eli:
Originally posted by SVTour98:
Hoping you guys can help me out here, I have a math problem that I cannot figure out for the life of me! And I'm sure most of you guys will know it in a heartbeat...

"True or false? If true, give a justification (not just an example). If false, give a counterexample. Assume a, b, and c are natural numbers.

part 1) If "a" is a factor of "b" then GCF (a,b) = a



true

this one's not too bad if you think about it. think about exactly what you're saying when you say GCF - "greatest factor." how can "a" have a factor thats bigger than itself?

Quote:


part 2) If GCF (a,b) = x and GCF (a,c) = x, then b = c "




false

a = 12
b = 9
c = 3


That's right, 1 is true and 2 is false. For 2, consider any three numbers a, b, and c that have a greatest common factor x. That does not imply that any of a, b, or c are the same number, although they could be. For example, 10, 15, and 25.

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