【备考每日练】最新GRE数学题之正数代数题
- 2015年11月25日10:41 来源:小站整理
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每日一练
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 possible value of n ?
A.8
B.10
C.12
D.14
E.16
正确答案
C D E
思路分析
We are told that n! =990*k, which means that n! must have all factors of 990 to be the multiple of 990, 990 = 2 * 5 * 3 * 3* 11,so product from 1 to n should have all the above numbers. n = 11 will have all the above numbers as factors, hence must have 11 too, so the least value of n is 11.n>=11.
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