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?

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

Given that:

x=150!, To solve the question we need the power of 5 in prime factorization of 150!.

Since

y is an integer greater than 0,

we shall have

150/5+150/5^2+150/5^3

=30+6+1

=37

Hence the answer is: D.