What is the greatest common divisor of positive integers m and n?
C1. m is a prime number
C2. 2n = 7m
I'll go with C.
1 - Insufficient. we don't know anything about n.
n=3 Greatest divisor is 3
n=2 Greatest divisor is 1
2 - insufficient, multiple values for this equation
Together - 2n = 7m.....given that 2n is even, 7m must also be even. However, we know that m is prime..therefore m must be 2 in order for 7m to be even.
m must be 2, and n must be 7.
I got B but now I see where i went wrong. Great explanation tl372!
originally i though
if 2n=7m, then
2n = some multiple of 7, 2, and any integer
7m = some multiple of 2, 7, and any integer
so can you conclude that 7 is the greatest common divisor?
or do you mean that the "any integer" can be equal and thus the greatest common divisor...
so if 2n = 140 then, 2, 7, 10
7m = 140, 7, 2, 10
GCD is 10. you could have an infinite number of GCD depending on the value of the integer selected.
But if m is prime and 7m is even, m=2. and the GCD is 7.