An element d in R is said to be a greatest common divisor of a and b if:
1) d|a and d|b
2) Whenever c|A and c|b then c|d.
Let d_1 and d_2 be two greatest common divisors of a and b in R.
From the definition of Greatest Common Divisor we have d_1|d_2 and d_2|d_1. Thus d_1 and d_2 are associates in R.