Question:
The number of subgroups of a cyclic group of order 12 is __________.
The number of subgroups of a cyclic group of order 12 is __________.
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For a cyclic group of order \( n \), the number of subgroups is equal to the number of divisors of \( n \).
Updated On: Dec 4, 2025
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Correct Answer: 6
Solution and Explanation
Let \( G \) be a cyclic group of order 12. The number of subgroups of a cyclic group is equal to the number of divisors of the order of the group.
The divisors of 12 are: 1, 2, 3, 4, 6, and 12.
Thus, the number of subgroups of a cyclic group of order 12 is the number of divisors of 12, which is 6.
The divisors of 12 are: 1, 2, 3, 4, 6, and 12.
Thus, the number of subgroups of a cyclic group of order 12 is the number of divisors of 12, which is 6.
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