Answer:
Given
a * b = H.C.F. of a and
and a and
b
=
H.C.F. of b and a = b * a
is
commutative.
Also
(a * b) * c = (H.C.F. of a and b) * c
=
a * (H.C.F. of b and c)
=
a * (b * c)
is
associative.
Let
e be the identity element of N.
H.C.F. of a
and e =
a divides
But
there is no number ?e? which is divisible by every natural number.
Hence
identity element does not exist in N.
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