求助

yunhaoll · 发表于 2008-4-13 15:48:00

求助

If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990,

what is the least possible value of n.

答案选11

一点思路都么有呀

依然jmy · 发表于 2008-4-13 16:00:00

990=2*3^2*5*11

11是990的最大质因数，要是990的multiple,必须含有11，

而2*3^2*5必然是1*2*3……*10的因子，所以1*2*3……*10*11必然为990的倍数，11也就是n的最小的取值

表达能力有限，不知道lz理解否？

Kristine · 发表于 2008-4-13 16:08:00

The product of all the integers is a multiple of 990. It mean the number is at least 990.

The 990 can be written as 3x3x11x10

It means the serial of consecutive integers at least has to include one multiple of 11.

huangyh03 · 发表于 2008-4-13 16:09:00

楼上正确，此类题从分解因子入手

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所属分类: GMAT考试

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