2. 外语
  3. How many positive integers n are there such that 30n is a divisor of (23)×(3)×(53)?

How many positive integers n are there such that 30n is a divisor of (23)×(3)×(53)?

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问题 How many positive integers n are there such that 30n is a divisor of (23)×(3)×(53)?
选项 A、8
B、6
C、18
D、9
E、None
答案D
解析 (23)×(3)×(53)=30×22×52要使30n是(23)×(3)×(53)的因子，那么n就必须22×52的因子，22×52有多少个不同的因子呢?利用因子个数的求法，共有(2+1)×(2+1)=9个，所以D是正确答案。
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