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Let **be the binary operation on N defi...

Let `**`be the binary operation on N defined by `a ** b = HdotCdotFdot`of a and b. Is `**`commutative? Is `**`associative? Does there exist identity for this binary operation on N?

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Check commutative ∗ is commutative if `a∗b=b∗a`
`a∗b=HCFof a & b`
`b∗a=HCF of b & a`
...
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