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?
A) 10
B) 11
C) 12
D) 13
E) 14
I was given an explanation that for me is way too complicated, as if it was written in Chinese. Can someone please explain it to me in an easier way? Thanks.
Answer: B
990 is a multiple of n! implies it must contain all the prime factors of 990
Largest prime factor of 990 is 11 implies n! must have 11 as a factor
Now since n! = 990x where x is integer it implies it can have prime factors more than 11 but not less than 11
Thus least possible value of n is thus 11
A) 10
B) 11
C) 12
D) 13
E) 14
I was given an explanation that for me is way too complicated, as if it was written in Chinese. Can someone please explain it to me in an easier way? Thanks.
Answer: B
990 is a multiple of n! implies it must contain all the prime factors of 990
Largest prime factor of 990 is 11 implies n! must have 11 as a factor
Now since n! = 990x where x is integer it implies it can have prime factors more than 11 but not less than 11
Thus least possible value of n is thus 11
