Question

How many zeroes are contained in 200!

Answer 1

How many zeroes are contained by 200
answer-2 zeroes

Answer 2

The number of zeros contained in the decimal representation of the factorial of any non- negative number n(n!) can be calculated by using the below formula

$\frac n5+\frac n {5^2}$ +…+$\frac n {5^m}$  where m should be such that $5^{m+1}$>n  

So now here n=200

Before substituting in the formula n=200, let us first find what should be m

So, based on the condition

$5^ {m+1}$>200  

The power of 5 that should result in a number that is greater than 200 is 54=625.

m+1=4 →m=4-1=3

m should be 3

Now substituting in the formula n=200 and m=3, we get

$\frac{200}{5}+\frac{200}{5^2}+\frac{200}{5^3}=40+8+1=49$  

Thus, the number of zeros contained in 200! is 49