If x is the product of the integers from 1 to 150, inclusive, and 5y is a factor of x, what is the greatest possible value of y?

Solution:

Given product of 150 numbers is x.

⇒1 . 2 . 3 . 4 .5 .......150 = x

This is denoted as the factorial of 150.

x = 150!

We need to find the powers of 5 that are there in 150!

150/5 + 150/ 5² + 150/5³

= 30 + 6 + 1

= 37

If x is the product of the integers from 1 to 150, inclusive, and 5y is a factor of x, what is the greatest possible value of y?

Summary:

If x is the product of the integers from 1 to 150, inclusive, and 5y is a factor of x, the greatest possible value of y is 37.