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If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, incl
If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, incl
admin
2009-05-19
34
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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