The number of generators of cyclic group of order 219 is __________
A. 144
B. 124
C. 56
D. 218
Answer:A
The number of generators of cyclic group of order 219 is __________
A. 144 B. 124 C. 56 D. 218
Explanation: 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.