# Discrete Mathematics GCD Question

Printable View

• February 5th 2010, 11:04 AM
jcornish
Discrete Mathematics GCD Question
Suppose a certain student’s ID number M satisfies
gcd(M, 2010) > gcd(M, 271) > 1.
Find all possible values for gcd(M, 2010). Be sure to explain your reasoning. [Note: both 271 and 67 are prime.]

I have gotten most of the way through the question....but will wait to see if anyone else has any insights. It is very possible that I am stuck because one of my steps lead me in the wrong direction...
• February 5th 2010, 11:48 AM
Roam
All greatest common divisors of (M, 2010) are multiples of 67. Since M is a multiple of both 271 and 67 you know that $M = 271 \times 67 \times x$, $\exists x \in Z$, so what do you think about x?