2. 外语
  3. Which of the following integers does NOT have a factor greater than 1 that is the square of an integer?

Which of the following integers does NOT have a factor greater than 1 that is the square of an integer?

admin2022-10-18  30
问题 Which of the following integers does NOT have a factor greater than 1 that is the square of an integer?
选项 A、100
B、128
C、72
D、54
E、42
答案E
解析 把选项中的数分解质因数后，如果每个质因子的指数都小于2，那么这个数便是答案。100=22×52。128=82×2，72=2×62，前三个选项都有能够表达为完全平方数的因子。许多考生在第四个选项上犯了错误，认为54=2×33，没有因子能够表达为完全平方数。其实不然，54=2×33，那么32必然也是54的因子。选项E：42=6×7，显然没有因子能够表达为完全平方数，所以选择E。
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