What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) 2n=7m
1) m is a prime number
2) 2n=7m
(1) If m is a prime number, then it may or may not be a prime factor of n. Hence the greatest common divisor may be either m or m n. Moreover, m and n are also not known. Insufficientabhasjha wrote:What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) 2n=7m
(2) If twice of one positive integer is 7 times another positive integer, then the former must have 7 as its factor, or n has 7 as one of its factor, for sure, whereas, m may or may not have 7 as one of its factor. Also, that the later must have 2 as its factor, or m has 2 as one of its factor, for sure, whereas, n may or may not have 2 as one of its factor. So, if n = 7 p and m = 2 q for some positive integers p and q, then their greatest common divisor is the greatest common divisor of the positive integers p and q that we don't know. Insufficient
Taken together
If m is prime, then q is 1, and the greatest common divisor of p and 1 is p. We don't know what's p. Still insufficient
[spoiler]E[/spoiler]
