Explanation If you have to count the number of zero’s in n!.
n/5 + n/(5^{2}) + n/(5^{3})….
Using the formula given above:
173/5 + 173/25 + 173/125 = 34 + 6 + 1 = 41.
Now lets verify this to grasp the concept,
All the numbers less than 173 which are divisible by 5 are:
170,165,160,155,150, 145, 140 , 135, 130, 125, 120,115,110,100,…..5
5x34, 5x33, 5x32, 5 x 31, 5^{2}x6, 5x29, 5x28,5x27,5x26,5^{3},5x24,5x23,5x22,5x21,5^{2}x4,….,5x3,5x2,5
If you count the number of 5’s in the above equation, you will find out that the answer is 41!