Question

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 1

The least possible values of n is:

11

Explanation:

We know that the product of first n natural numbers is: n!

Now, we are asked to find the minimum value of n such that n! is a multiple of 990.

This means that:

`n!=990k`

Now we know that:

`990=2* 3* 3* 5* 11`

Now we know that we obtain all of these factors when n is minimum 11.

Since,

`11!=1* 2* 3* 4* 5* 6* 7* 8* 9* 10* 11`

This means that :

`n\geq 11`