Let $n_1,n_1,\ldots,n_k\in\mathbb Z$ be integers. The simultanous greatest common divisor of all these numbers can be calculated by the recursive formula
$$\gcd(n_1,\ldots,n_k):=\gcd(\gcd(n_1,\ldots,n_{k-1}),n_k).$$
This calculation is independent of the order, in which the recursive formula is used, following the associativity and commutativity of the $\gcd$. In particular, for any integers $a,b,c\in\mathbb Z$ we have $$\gcd(\gcd(a,b),c))=\gcd(a,\gcd(b,c))$$ and $$\gcd(a,b)=\gcd(b,a).$$
Proofs: 1
