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CSS Pure Mathematics QUESTION #1276
Question 1
The order of the cyclic subgroup generated by \(\bar{6}\) in \(\mathbb{Z}_{18}\) is:
  • 2
  • 3✔️
  • 6
  • 9
Correct Answer Explanation
The order of \(\bar{a}\) in \(\mathbb{Z}_n\) is \(\dfrac{n}{\gcd(n,a)}\). Here \(n=18\), \(a=6\): order \(=\dfrac{18}{\gcd(18,6)}=\dfrac{18}{6}=3\).