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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

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))

2

10

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