  This research introduces a gcd-pair in $\mathbb{Z}_n$ which is an unordered
pair $\{[a]_n, [b]_n\}$ of elements in $ \mathbb{Z}_n $ such that $0\leq a,b <
n$ and the greatest common divisor $\gcd(a,b)$ divides $ n $. The properties of
gcd-pairs in $ \mathbb{Z}_n $ and their graph representations are investigated.
We also provide the counting formula of gcd-pairs in $ \mathbb{Z}_n $ and its
subsets. The algorithms to find, count and check gcd-pairs in $ \mathbb{Z}_{n}$
are included.
