2. 外语
  3. For how many positive integers n less than 40 is the number of positive factors of n equal to 6？

For how many positive integers n less than 40 is the number of positive factors of n equal to 6？

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问题 For how many positive integers n less than 40 is the number of positive factors of n equal to 6？
选项 A、4
B、5
C、6
D、7
E、8
答案B
解析 根据因数个数的计算，
6=3×2=(2+1)×(1+1)
=6×1=(5+1)×(1+0)
即有6个因数的数为一个质因数平方与另一个质因数的乘积，或一个质因数的5次方。
可能的数：
22×3=12
22×5=20
22×7=28
32×2=18
25=32
故共有5个可能的数，答案为B。
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