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