(b) 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.]
(c) Suppose that the ID number M from part (b) lies between 10020000 and 10030000.
Find M. Be sure to explain your reasoning.
The Attempt at a Solution
So I got b) (I think), gcd(M, 2010) must be greater than 271, as 271 is prime so gcd(M, 271) must be 1 or 271, and it's greater than 1. So I found all the divisors of 2010 which are greater than 271. (Being 2010, 1005, 670, 402, and 335) I think that's correct, though I'm not entirely sure.
As for c), I really have no idea how to find that, and was hoping for a nudge in the right direction