Let $\ast$ be the binary operation on $N$ defined by $a \ast b=H.C.F.$ of a and b. Is $\ast$ commutative? Is $\ast$ associative? Does there exist identity for this binary operation on $N$?

Question

$\begin{array}{1 1} \text{Not Commutative, Not Associative, Identity Exists} \\ \text{Not Commutative, Not Associative, Identity Does not Exist} \\ \text{Commutative, Associative, Identity Exists} \\ \text{Commutative, Associative, Identity Does not Exist} \end{array}$