# Gcd associativity

1. Mar 26, 2007

### lordy12

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. Mar 27, 2007

### HallsofIvy

Staff Emeritus
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).