If n = pqr, where p, q, and r are three different positive prime numbers, how ma

游客2025-02-24 52

问题 If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, including 1 and n?

选项 A、3
B、5
C、6
D、7
E、8

答案 E

解析若n=pqr，其中p，q，r是3个不同的正质数(positive prime numbers)，n有多少个不同的因子，包括1和n?
解：本题的正确答案为(E)。由因子数求解公式可得n=p×q×r，当p，q，r为质数时n的因子数为(1+1)(1+1)(1+1)=8个。

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