1 1 Pavanagg Asked: May 27, 20222022-05-27T19:19:21+05:30 2022-05-27T19:19:21+05:30In: Mathematics For a cyclic group of order 420, the number of generators are 1 1 For a cyclic group of order 420, the number of generators are (a) 66 (b) 96 (c) 86 (d) 76 Share Facebook 1 Answer Voted Oldest Recent ADMIN 2 2022-05-27T19:39:03+05:30Added an answer on May 27, 2022 at 7:39 pm 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 Leave an answerCancel replyYou must login to add an answer. Username or email* Password* Remember Me! Forgot Password?

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