SOLUTION: if 3 is the greatest common divisor of positive integers r and s, what is the greatest common divisor of 2r and 2s? (A) 2 (B) 3 (C) 4 (D) 6 (E) 12

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: if 3 is the greatest common divisor of positive integers r and s, what is the greatest common divisor of 2r and 2s? (A) 2 (B) 3 (C) 4 (D) 6 (E) 12       Log On


   

Question 3426: if 3 is the greatest common divisor of positive integers r and s, what is the greatest common divisor of 2r and 2s?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Since r = 3p, s = 3q, and (p,q) = 1 (relative prime)
we see that 2r = 6p, s = 6q and (p,q) = 1

This means(2r,2s) = 6
Answer: D