x is the product of each integer from 1 to 100, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
Choose the correct choice from the following answers.
A) 5
B) 6
C) 8
D) 10
E) 12
The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:   n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n   x = 1*2*3....*100 = 100!   No. of trailing zeros in 100! = 100/5 + 100/5^2 = 20+4= 
<gadget id="calculator">20+4</gadget>
<output>24</output>
24   100^k= 10^2k → k = 24/2= 
<gadget id="calculator">24/2</gadget>
<output>12</output>
12   12
<result>E</result>
x is the product of each integer from 1 to 100, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?