Gcd associativity

  • Thread starter lordy12
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  • #1
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1.Show gcd(a,b,c) = gcd(a, gcd(b,c))



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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.
 

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  • #2
HallsofIvy
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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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