# Program to find number m such that it has n number of 0s at end in Python

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Suppose we have a number n. We have to find smallest number m, such that factorial of m has at least n number of 0s.

So, if the input is like n = 2, then the output will be 10 because 10! = 3628800 and 9! = 362880, minimum number with 2 zeros is 10.

To solve this, we will follow these steps −

• Define a function count_fives() . This will take n
• cnt := 0
• while n > 0, do
• n := floor of (n / 5)
• cnt := cnt + n
• return cnt
• From the main method, do the following −
• left := 1
• right := 5^24
• while right - left > 5, do
• mid := floor of ((right + left) / 10) * 5
• fives := count_fives(mid)
• if fives is same as n, then
• right := mid
• left := right - 5
• come out from the loop
• otherwise when fives < n, then
• left := mid
• otherwise,
• right := mid
• return right

## Example

Let us see the following implementation to get better understanding −

def count_fives(n):
cnt = 0
while n > 0:
n = n // 5
cnt += n
return cnt

def solve(n):
left = 1
right = 5**24
while right - left > 5:
mid = int((right + left) / 10) * 5
fives = count_fives(mid)
if fives == n:
right = mid
left = right - 5
break
elif fives < n:
left = mid
else:
right = mid
return right

n = 2
print(solve(n))

## Input

2


## Output

10
Updated on 25-Oct-2021 08:08:24