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August 27th, 2009, 01:57 PM   #1
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Match Question sorrry if posted in the wrong section

can anyone tell me how to figure this out (without just plugging in the values experimentally)?

If x and y are positive integers such that the greatest common factor of x^2y^2 and xy^3 is 45, then which of the following could y equal?
a. 45
b. 15
c. 9
d. 5
e. 3
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August 29th, 2009, 10:35 AM   #2
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Re: Match Question sorrry if posted in the wrong section

I'm not a number guy, but think that's how you do it.

You must have cause if they were equal you would have that and then the greatest common factor would be . but is not an integer.

Now, the greatest common factor of and is . Then you have that wich gives you that .

If you find any mistake tell me
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September 1st, 2009, 03:56 AM   #3
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Since gcd(xy, xy) = xy(gcd(x, y)) = 45 = 3(5), 45 is a multiple of y, and so y = 1 or 3. Hence, of the alternative values for y listed, only 3 is possible.
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September 1st, 2009, 06:49 PM   #4
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Re: Match Question sorrry if posted in the wrong section

I plugged into my latest fav site wolframalpha.com and it confirms the earlier post

input box: gcd(xy, xy)=45

it reports integer solutions at x,y = (45,1), (5,3) and shows a nice plot via the power of Mathematica behind it
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