
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 27th, 2009, 01:57 PM  #1 
Newbie Joined: Aug 2009 Posts: 1 Thanks: 0  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 
August 29th, 2009, 10:35 AM  #2 
Senior Member Joined: Feb 2009 Posts: 172 Thanks: 5  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 
September 1st, 2009, 03:56 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,755 Thanks: 2137 
Since gcd(x²y², xy³) = xy²(gcd(x, y)) = 45 = 3²(5), 45 is a multiple of y², and so y = 1 or 3. Hence, of the alternative values for y listed, only 3 is possible.

September 1st, 2009, 06:49 PM  #4 
Senior Member Joined: Aug 2008 From: Blacksburg VA USA Posts: 350 Thanks: 7 Math Focus: primes of course  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(x²y², xy³)=45 it reports integer solutions at x,y = (45,1), (5,3) and shows a nice plot via the power of Mathematica behind it 

Tags 
match, question, section, sorrry, wrong 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is there something wrong with this question?  perfect_world  Algebra  5  September 2nd, 2013 05:26 AM 
Match the Parabola  HellBunny  Algebra  2  March 21st, 2012 09:33 AM 
Vector question. What am I doing wrong?  spa0324  Advanced Statistics  0  May 25th, 2009 10:05 AM 
Trigonometric equation doesn’t match the graph  Nazz  Algebra  4  May 14th, 2009 08:21 AM 