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This research introduces a gcd-pair in $\mathbb{Z}_n$ which is an unorderedpair $\{[a]_n, [b]_n\}$ 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 ofgcd-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 itssubsets. The algorithms to find, count and check gcd-pairs in $ \mathbb{Z}_{n}$are included.

gcd-Pairs in $\mathbb{Z}_{n}$ and their graph representations