Suppose a certain student's ID number, M satisfies:
gcd(M, 2010) > gcd(M, 271) > 1

Find all possible values for gcd(M, 2010).

I know how to do gcd and Euclid's algorithm, but I don't see how to find all the values. Can someone point me in the right direction?

Here's what I was thinking:

If gcd(M, 271) > 1, then M is a multiple of 271 and not prime. And if gcd(M, 2010) is greater than that, then gcd(M, 2010) is somehow related.

I can't figure this out.

Thanks for the help!