surya167 Posted September 25, 2007 Share Posted September 25, 2007 What is the greatest common divisor of positive integers m and n ? 1) m is a prime number 2) 2n = 7m Quote Link to comment Share on other sites More sharing options...
krusta80 Posted September 25, 2007 Share Posted September 25, 2007 What is the greatest common divisor of positive integers m and n ? 1) m is a prime number 2) 2n = 7m GCD(m,n) is equal to the product of all similar prime factors of m and n. (1) "m is a prime number" "n" can either have m as a factor or not, so INSUFFICIENT. (2) "2n = 7m" This only tells us that n has one more 7 in its prime product than m and that m has one more 2 in its prime product as n. Finally, all other prime numbers appear the same number of times in m and n. This leaves open an inifinite number of possible GCD's. INSUFFICIENT (1) and (2) If m is prime, then it has to be 2, since m has to have one more 2 in its prime product than n. If m is 2, then n is 7, and GCD(m,n) = 1 Thanks, lsr! I was doing the GCD for 2n and 7m. :) C Quote Link to comment Share on other sites More sharing options...
lsr Posted September 25, 2007 Share Posted September 25, 2007 Krusta, I agree with everything but the last line. GCD(2,7)=1 Quote Link to comment Share on other sites More sharing options...
alactraz Posted September 25, 2007 Share Posted September 25, 2007 I agree with lsr GCD is the largest positive integer that divides both numbers without remainders. For example, gcd(12, 18) = 6, gcd(−4, 14) = 2 and gcd(5, 0)=5 adn gcd(7,2)=1 Quote Link to comment Share on other sites More sharing options...
surya167 Posted September 25, 2007 Author Share Posted September 25, 2007 GCD of coprime numbers is always one.. I guess krusta has found out the LCM here.. LCM of coprime numbers is their product Quote Link to comment Share on other sites More sharing options...
krusta80 Posted September 25, 2007 Share Posted September 25, 2007 GCD of coprime numbers is always one.. I guess krusta has found out the LCM here.. LCM of coprime numbers is their product Actually, I was still thinking about 2n and 7m. lol Sorry, guys! I thought it was nice until then at least. hehe Quote Link to comment Share on other sites More sharing options...
nikiforos Posted September 25, 2007 Share Posted September 25, 2007 My Ans is C 1. n can be any value, so insuff 2. if 2n = 7m, then we know that n has to be a factor of 7 and m has to be a factor of 2. so 2n = 2.7.k and 7m = 7.2.l where k,l are integers To find out the gcd we have to find other common factors of k, l. So this stmt by itself is insufficient Combinin both statements, we know that m is prime and that it has to be a factor of 2. so m = 2, n = 7 GCD = 14 so sufficient Quote Link to comment Share on other sites More sharing options...
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