How many integers between 99 and 365 are there such that they have 3 divisors?

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问题 How many integers between 99 and 365 are there such that they have 3 divisors?

选项 A、2
B、4
C、6
D、8
E、10

答案B

解析据因数个数公式n=(a₁+1)(a₂+1)…(a_n+1)=3，可知a₂=2，即将所求整数做质因数分解后，只有一个质因数，且该整数为此质因数的平方。于是本题变为：99到365之间有多少整数是质数的平方?99后面的完全平方数是100=10²；365前面的完全平方数是361=19²；那么10到19之间有质数11、13、1 7、19这4个，即99到365之间有4个质数的平方。答案为B选项。

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How many integers between 99 and 365 are there such that they have 3 divisors?

GRE QUANTITATIVE

GRE

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