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Re: If n is a positive number Gmat prep [#permalink]
07 Nov 2009, 12:18
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? A. 10 B. 11 C. 12 D. 13 E. 14
We are told that \(n!=990*k=2*5*3^2*11*k\) which means that n! must have all factors of 990 to be the multiple of 990, hence must have 11 too, so the least value of n is 11 (notice that 11! will have all other factors of 990 as well, otherwise the least value of n would have been larger).