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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?
admin
2019-05-11
62
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:
2
2
×3=12
2
2
×5=20
2
2
×7=28
3
2
×2=18
2
5
=32
故共有5个可能的数,答案为B。
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