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The number of generators of cyclic group of order 219 is __________

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The number of generators of cyclic group of order 219 is __________

(a) 144

(b) 124

(c) 56

(d) 218

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Enquiry is from Cyclic Groups topic in chapter Groups of Discrete Mathematics

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The correct option is (a) 144

For explanation I would say: The number of generators of a cyclic group of order n is equal to the number of integers between 1 and n that are relatively prime to n.Namely, the number of generators is equal to ϕ(n), where ϕ is the Euler totient function. We know that G is a cyclic group of order 219. Hence, the number of generators of G is ϕ(219) = ϕ(3)ϕ(73) = 3⋅73 = 144.

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