Problem Solving

Hi all,

I'm a newbie here so I hope this is the right place to post. I wasn't sure how to derive the answer for the following question, and I hope someone here can help:

Q: If n is a positive integer, and the product of all integers from 1 to n is a multiple of 990, what is the least possible value of n?

A: 10 11 12 13 14

I know the answer is 11, but how do I get to the answer using an efficient method?

Thanks!

paradox wrote:
Q: If n is a positive integer, and the product of all integers from 1 to n is a multiple of 990, what is the least possible value of n?

A: 10 11 12 13 14

I know the answer is 11, but how do I get to the answer using an efficient method?

Thanks!

The Bold statement implies n factorial

So n! = kx990 =k x 9x10x11

Hence 11 has to become the least value

Pardon my ignorance, but how do you know that there are no numbers lower than 11 in the sequence that could be factors of 990?

paradox wrote:Pardon my ignorance, but how do you know that there are no numbers lower than 11 in the sequence that could be factors of 990?

There definitely are numbers lower than 990 that will be factors of 990. However the question states that n! is a multiple of 990. Now 990 can be split into 9x10x11 with 11 being the highest prime. Therefore the only way you could get 11 in the product was if it was actually part of n.
Therefore the smalles possible value of n had to be 11