Let `**` a binary operation on `NN` given by `a**b=H.C.F (a,b)` for all `a,binNN`, write the value

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Let * be the binary operation on N defined by a*b=HCF of a and b. Does there exist identity for this

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Let * be the binary operation on N defined by a*b=H.C.F of a&b. Is * commutative? Is * associative?

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Let * be a binary operation on N defined by a*b= HCF of a and b Is * commutative? Is * associative?

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