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

Answer:

The least possible values of n is:

                                   11

Step-by-step 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:

$990=2\times 3\times 3\times 5\times 11$

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

Since,

$11!=1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9\times 10\times 11$

This means that :

$n\geq 11$