# Q. 8 Let ∗ be the binary operation on N defined by a ∗ b = H.C.F. of a and b. Is ∗ commutative? Is ∗ associative? Does there exist identity for this binary operation on N?

a ∗ b = H.C.F. of a and b for all

H.C.F. of a and b = H.C.F of b and a for all

Hence, operation  ∗  is commutative.

For   ,

Hence,  ∗ is associative.

An element  will be identity for operation *  if   for .

Hence, the operation * does not have any identity in N.

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