1 Pavanagg Asked: May 27, 20222022-05-27T19:19:21+05:30 2022-05-27T19:19:21+05:30In: MathematicsFor a cyclic group of order 420, the number of generators are1For a cyclic group of order 420, the number of generators are(a) 66(b) 96(c) 86(d) 76 ShareFacebook1 AnswerVotedOldestRecent 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 7No. 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=96Leave 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