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Math Help - Discrete Mathematics GCD Question

  1. #1
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    Discrete Mathematics GCD Question

    Suppose a certain studentís 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...
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  2. #2
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    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?
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