Group $G$ with $ord(G)=319$ is a cyclic group

Question

Let $G$ be a group with $ord(G)=319$. Proove that $G$ is a cyclic group.

Answer: $ord(G)=319=11*29=n$, the Euler's totient function gives $\phi(n)=\phi(11*29)=\phi(11)*\phi(29)=10*28$. Since $gcd(319,280)=1$, $G$ is a cyclic group.

[Related:Answer from Nicky Hekster]