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Gcd associativity

  1. Mar 26, 2007 #1
    1.Show gcd(a,b,c) = gcd(a, gcd(b,c))

    2. Relevant equations

    3. My attempt is that gcd(a,b,c) can be written as the product of their prime factors. Lets say x is that product. The thing is, I know how to prove this using prime factorization but there has to be another method concerning linear combinations. Like gcd(a,b,c) = ax + by+ cz.
  2. jcsd
  3. Mar 27, 2007 #2


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    Why not just say a= nx, b= ny, c= nz where n= gcd(a,b,c).
    Of course, you also have b= mp, c= mq where m= gcd(b,c).
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