GRE数学试题

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

参考答案
正确答案：C ，D， E。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.