enigma123
What is the greatest common factor of positive integers x and y?
(1) x and y share only one common factor.
(2) x and y are unique prime numbers.
Below is my solution. Struggling to understand the official answer. Can someone please help?
Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.
Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.
Hence, I went for B, which is not the case.
What is the greatest common factor of positive integers x and y?(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.
(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.
Answer: D.
Hope it's clear.