2. 外语
  3. When 66, 90, 150 are divided by the positive integer n respectively, they have the same remainder, which of the following could

When 66, 90, 150 are divided by the positive integer n respectively, they have the same remainder, which of the following could

admin2022-12-19  53
问题 When 66, 90, 150 are divided by the positive integer n respectively, they have the same remainder, which of the following could be the largest value of n?
选项 A、3
B、4
C、6
D、8
E、12
答案E
解析 如果不知道如何求解，可以用代入排除法比较，求出最大的一个数。这类题目通常利用同余概念来求解，将三个数中任意两个数相减，其差就能够被n整除。
90-66=24，24能够被n整除；
150-90=60，60也能够被n整除；
两个数均能够被n整除，现在要求n的最大值，那么当然是找24和60的最大公约数。
24=23×3，
60=22×3×5，
最大公约数为22×3=12，所以选择E。
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