Answer :
Final answer:
The number of subgroups of Z_1800, a cyclic group, is determined by the number of divisors of 1800 which is 36. Therefore, none of the provided options are correct.
Explanation:
The question asks for the number of subgroups of Z_1800. The number of subgroups of a cyclic group Z_n is determined by the number of divisors of n. In the case of n=1800, its divisors are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, and 1800. Counting these divisors, we find that there are 36 of them. Therefore, there are 36 subgroups of Z_1800, so none of the provided options in the question are correct.
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