For a cyclic group of order 420, the number of generators are

(a) 66

(b) 96

(c) 86

(d) 76

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Correct option is (b) 96.

Explanation:group of order = 420

prime factors of 420 = 2 x 2 x 3 x 5 x 7

prime factors are 2, 3, 5 and 7

No. of generators = 420× (1-1/2)(1-1/3)(1-1/5)(1-1/7)

=420/2 x 2/3 x 4/5 x 6/7

=96