B166418 wrote:If N is posstive integer and product of all integers from 1 to N is multiple of 990 ,what is least possible value of N
A) 10
B) 11
C) 12
D) 13
E) 14
Here are the original answer choices to the question.
A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Similarly, we can say:
If N is is a multiple of k, then k is "hiding" within the prime factorization of N
Examples:
24 is divisible by
3 <--> 24 = 2x2x2x
3
70 is divisible by
5 <--> 70 = 2x
5x7
330 is divisible by
6 <--> 330 =
2x
3x5x11
56 is divisible by
8 <--> 56 =
2x
2x
2x7
So, if if some number is a multiple of 990, then
990 is hiding in the prime factorization of that number.
Since 990 = (2)(3)(3)(5)(11), we know that one 2, two 3s, one 5 and one 11 must be hiding in the prime factorization of our number.
For 11 to appear in the product of all the integers from 1 to n, n must equal 11 or more.
So, the answer is
B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
