📺 Watch Video Explanation:
Check commutativity and associativity
Given:
\( a * b = \gcd(a,b), \quad a,b \in \mathbb{N} \)
Commutativity:
\( \gcd(a,b) = \gcd(b,a) \)
✔ Operation is commutative
Associativity:
\( \gcd(\gcd(a,b),c) = \gcd(a,\gcd(b,c)) \)
✔ Operation is associative
Conclusion:
✔ The operation is both commutative and associative on \( \mathbb{N} \).