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.