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A positive integer with exactly two different divisors greater than 1 must beA、a
A positive integer with exactly two different divisors greater than 1 must beA、a
游客
2025-02-24
31
管理
问题
A positive integer with exactly two different divisors greater than 1 must be
选项
A、a prime
B、an even integer
C、a multiple of 3
D、the square of a prime
E、the square of an odd integer
答案
D
解析
仅有两个不同的大于1的因子的正整数一定是:
解:本题的正确答案是(D)。大多数考生在做本题时都用了排除法,虽然用排除法也可把本题做对,但是这种方法却是不对的。考生在解答本题时一定要正确理解题意,该题问的是具有两个大于1的不同因子的数一定是什么样的数,并不一定这样的数都具有两个大于1的不同因子。因此解答本题时不应当用找反例的排除法,而是找这个选项是否包含了所有的具有这个性质的数。这样就排除了诸如(E)这类的选项,因为4也具有这个性质,而它不是奇数的平方。具有两个不同的大于1的因子的数,共有3个因子而因子数求解公式中只有质数的平方才具有3个因子。所以(D)是正确答案。请注意问题中的“must be”。
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