The number of generators of the cyclic group G of order 8 is

Calculation:

Let a cyclic group G of order 8 generated by an element a, then 

⇒ o(a) = o(G) = 8

To determine the number of generators of G,

Evidently, G = {a, a², a³, a⁴, a⁵, a⁶, a⁷, a⁸ = e}

An element a^m ∈ G is also a generator of G is HCF of m and 8 is 1.

HCF of 1 and 8 is 1, HCF of 3 and 8 is 1, HCF of 5 and 8 is 1, HCF of 7 and 8 is 1.

Hence, a, a3, a5, a⁷ are generators of G.

Therefore, there are four generators of G.