# Find N from the value of N!

Given a number K which represents the factorial of a number N, the task is to find the value of N.
Note: K < 1018

Examples:

Input: K = 120
Output: 5
Explanation:
5! = 1 * 2 * 3 * 4 * 5 = 120

Input: K = 6
Output: 3
Explanation:
3! = 1 * 2 * 3 = 6

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: It is given that the value of N! is less than 1018. On observation we can see that this is true only for N <= 18. Therefore we can precompute values of factorials from 1 to 18 and store it in a Hash Table or Map. After precomputation, for every value of N!, the corresponding N is returned in constant time.

Below is the implementation of the above approach:

## C++

 `// C++ program to find a number such that ` `// the factorial of that number is given ` ` `  `#include "bits/stdc++.h" ` `#define ll long long int ` `using` `namespace` `std; ` ` `  `// Map to precompute and store the ` `// factorials of the numbers ` `map m; ` ` `  `// Function to precompute factorial ` `int` `precompute() ` `{ ` ` `  `    ``ll fact = 1; ` `    ``for` `(ll i = 1; i <= 18; i++) { ` ` `  `        ``// Calculating the factorial for ` `        ``// each i and storing in a map ` `        ``fact = fact * i; ` `        ``m[fact] = i; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// Precomputing the factorials ` `    ``precompute(); ` ` `  `    ``int` `K = 120; ` `    ``cout << m[K] << endl; ` ` `  `    ``K = 6; ` `    ``cout << m[K] << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find a number such that ` `// the factorial of that number is given ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `  `  `// Map to precompute and store the ` `// factorials of the numbers ` `static` `Map m = ``new` `HashMap(); ` `  `  `// Function to precompute factorial ` `static` `void` `precompute() ` `{ ` `  `  `    ``int` `fact = ``1``; ` `    ``for` `(``int` `i = ``1``; i <= ``18``; i++) { ` `  `  `        ``// Calculating the factorial for ` `        ``// each i and storing in a map ` `        ``fact = fact * i; ` `        ``m.put(fact, i); ` `    ``} ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``// Precomputing the factorials ` `    ``precompute(); ` `  `  `    ``int` `K = ``120``; ` `    ``System.out.print(m.get(K) +``"\n"``); ` `  `  `    ``K = ``6``; ` `    ``System.out.print(m.get(K) +``"\n"``); ` `  `  `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 program to find a number such that  ` `# the factorial of that number is given  ` ` `  `# Map to precompute and store the  ` `# factorials of the numbers  ` `m ``=` `{};  ` ` `  `# Function to precompute factorial  ` `def` `precompute() : ` ` `  `    ``fact ``=` `1``;  ` `    ``for` `i ``in` `range``(``1``, ``19``) : ` ` `  `        ``# Calculating the factorial for  ` `        ``# each i and storing in a map  ` `        ``fact ``=` `fact ``*` `i;  ` `        ``m[fact] ``=` `i;  ` `         `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``# Precomputing the factorials  ` `    ``precompute();  ` ` `  `    ``K ``=` `120``;  ` `    ``print``(m[K]);  ` ` `  `    ``K ``=` `6``;  ` `    ``print``(m[K]) ;  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# program to find a number such that ` `// the factorial of that number is given ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` `   `  `// Map to precompute and store the ` `// factorials of the numbers ` `static` `Dictionary<``int``, ``int``> m = ``new` `Dictionary<``int``, ``int``>(); ` `   `  `// Function to precompute factorial ` `static` `void` `precompute() ` `{ ` `   `  `    ``int` `fact = 1; ` `    ``for` `(``int` `i = 1; i <= 18; i++) { ` `   `  `        ``// Calculating the factorial for ` `        ``// each i and storing in a map ` `        ``fact = fact * i; ` `        ``m.Add(fact, i); ` `    ``} ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``// Precomputing the factorials ` `    ``precompute(); ` `   `  `    ``int` `K = 120; ` `    ``Console.Write(m[K] +``"\n"``); ` `   `  `    ``K = 6; ` `    ``Console.Write(m[K] +``"\n"``);   ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```5
3
```

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Improved By : AnkitRai01, 29AjayKumar