Greatest Common FactorDate: 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. 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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