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Check if a given number is factorial of any number
  • Last Updated : 27 Nov, 2019

Given a number n, the task is to determine whether n can be a factorial of some number x

Examples:

Input: N = 24
Output: Yes
Explanation: 4! = 24

Input: N = 25
Output: No

Approach:

    Divide x by 2, divide by 3, and so on, until you cannot divide further. If you reach the number 1, then it’s factorial number else not.

Below is the implementation of the above approach:

C++




// C++ implementation for 
// the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to check if 
// the given number is a 
// factorial of any number
bool isFactorial(int n)
{
  for (int i = 1;; i++) {
    if (n % i == 0) {
      n /= i;
    }
    else {
      break;
    }
  }
  
  if (n == 1) {
    return true;
  }
  else {
    return false;
  }
}
  
// Driver Code
int main()
{
  int n = 24;
  
  bool ans = isFactorial(n);
  if (ans == 1) {
    cout << "Yes\n";
  }
  else {
    cout << "No\n";
  }
  
  return 0;
}


Java




// Java implementation for the above approach 
class GFG
{
  
    // Function to check if the given number 
    // is a factorial of any number 
    static boolean isFactorial(int n) 
    
        for (int i = 1;; i++) 
        
            if (n % i == 0
            
                n /= i; 
            
            else 
            
                break
            
        
      
        if (n == 1
        
            return true
        
        else 
        
            return false
        
    
      
    // Driver Code 
    public static void main (String[] args) 
    
        int n = 24
        boolean ans = isFactorial(n); 
          
        if (ans == true
        
            System.out.println("Yes"); 
        
        else
        
            System.out.println("No"); 
        
    
}
  
// This code is contributed by AnkitRai01


Python3




# Python3 implementation of the approach 
  
# Function to check if 
# the given number is a 
# factorial of any number 
def isFactorial(n) :
    i = 1;
    while(True) :
          
        if (n % i == 0) :
            n //= i;
              
        else :
            break
              
        i += 1;
  
    if (n == 1) :
        return True
      
    else :
        return False
  
# Driver Code 
if __name__ == "__main__"
    n = 24
    ans = isFactorial(n); 
      
    if (ans == 1) :
        print("Yes"); 
  
    else :
        print("No"); 
  
# This code is contributed by kanugargng


C#




// C# implementation for the above approach
using System;
      
class GFG
{
  
    // Function to check if the given number 
    // is a factorial of any number 
    static Boolean isFactorial(int n) 
    
        for (int i = 1;; i++) 
        
            if (n % i == 0) 
            
                n /= i; 
            
            else
            
                break
            
        
      
        if (n == 1) 
        
            return true
        
        else
        
            return false
        
    
      
    // Driver Code 
    public static void Main (String[] args) 
    
        int n = 24; 
        Boolean ans = isFactorial(n); 
          
        if (ans == true
        
            Console.WriteLine("Yes"); 
        
        else
        
            Console.WriteLine("No"); 
        
    
}
  
// This code is contributed by 29AjayKumar


Output:

Yes

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