If n is a positive integer and the product of all

by **Guest** Thu Aug 02, 2007 9:59 pm

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?
Answer is 11

Is there an easy way to get to this answer?

by **GMAT 2007** Thu Aug 02, 2007 10:18 pm

The key here is to look for the prime factors of 990 .

990 = 2*3*3*5*11

Since the product is multiple of 990, so it should have all the prime factors present in it. If you notice 11 is one of them, and it is prime too, so the least possible value of n is 11.

Hope it helps

GMAT 2007

by **dbernst** Fri Aug 03, 2007 12:47 am

GMAT 2007 IN DA' HOUSE!

by **GMAT 2007** Fri Aug 03, 2007 1:15 am

Thanks Dan