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Find the next Factorial greater than N
  • Last Updated : 12 Apr, 2021

Given a number N (≤ 1018), the task is to find the next factorial number greater than N.
Examples: 
 

Input: N = 24 
Output: 120 
Explanation: 
As 4! = 24. So the next number which factorial and greater than 24 is 5!, which is 120
Input: N = 150 
Output: 720 
Explanation: 
As 5! = 120. So the next number which factorial and greater than 150 is 6!, which is 720. 
 

 

Approach: 
 

  1. Precompute the factorial of all number upto 20 in an array as 20! > 1018.
  2. Traverse the factorial array and find the value which is just greater than N as the required next factorial number.

Below is the implementation of above approach: 
 

C++




// C++ implementation of the above approach
 
#include "bits/stdc++.h"
using namespace std;
 
// Array that stores the factorial
// till 20
long long fact[21];
 
// Function to pre-compute
// the factorial till 20
void preCompute()
{
 
    // Precomputing factorials
    fact[0] = 1;
 
    for (int i = 1; i < 18; i++)
        fact[i] = (fact[i - 1] * i);
}
 
// Function to return the next
// factorial number greater than N
void nextFactorial(int N)
{
    // Traverse the factorial array
    for (int i = 0; i < 21; i++) {
 
// Find the next just greater
// factorial than N
        if (N < fact[i]) {
 
            cout << fact[i];
            break;
        }
    }
}
 
// Driver Code
int main()
{
    // Function to precalculate
    // the factorial till 20
    preCompute();
 
    int N = 120;
 
    // Function call
    nextFactorial(N);
 
    return 0;
}

Java




// Java implementation of the above approach
class GFG {
     
// Array that stores the factorial
// till 20
final static int fact[] = new int[21];
 
    // Function to pre-compute
    // the factorial till 20
    static void preCompute()
    {
     
        // Precomputing factorials
        fact[0] = 1;
     
        for (int i = 1; i < 18; i++)
            fact[i] = (fact[i - 1] * i);
    }
     
    // Function to return the next
    // factorial number greater than N
    static void nextFactorial(int N)
    {
        // Traverse the factorial array
        for (int i = 0; i < 21; i++) {
     
            // Find the next just greater
            // factorial than N
            if (N < fact[i]) {
     
                System.out.println(fact[i]);
                break;
            }
        }
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        // Function to precalculate
        // the factorial till 20
        preCompute();
     
        int N = 120;
     
        // Function call
        nextFactorial(N);
    }
     
}
 
// This code is contributed by AnkitRai01

Python3




# Python3 implementation of the above approach
 
# Array that stores the factorial
# till 20
fact = [0] * 21
 
# Function to pre-compute
# the factorial till 20
def preCompute():
 
    # Precomputing factorials
    fact[0] = 1
 
    for i in range(1, 18):
        fact[i] = (fact[i - 1] * i)
 
# Function to return the next
# factorial number greater than N
def nextFactorial(N):
  
    # Traverse the factorial array
    for i in range(21):
 
# Find the next just greater
# factorial than N
        if N < fact[i]:
 
            print(fact[i])
            break
 
# Driver Code
# Function to precalculate
# the factorial till 20
preCompute()
 
N = 120
 
# Function call
nextFactorial(N)
 
# This code is contributed by divyamohan123

C#




// C# implementation of the above approach
using System;
 
class GFG {
     
    // Array that stores the factorial
    // till 20
    static int []fact = new int[21];
 
    // Function to pre-compute
    // the factorial till 20
    static void preCompute()
    {
     
        // Precomputing factorials
        fact[0] = 1;
     
        for (int i = 1; i < 18; i++)
            fact[i] = (fact[i - 1] * i);
    }
     
    // Function to return the next
    // factorial number greater than N
    static void nextFactorial(int N)
    {
        // Traverse the factorial array
        for (int i = 0; i < 21; i++) {
     
            // Find the next just greater
            // factorial than N
            if (N < fact[i]) {
     
                Console.WriteLine(fact[i]);
                break;
            }
        }
    }
     
    // Driver Code
    public static void Main (string[] args)
    {
        // Function to precalculate
        // the factorial till 20
        preCompute();
     
        int N = 120;
     
        // Function call
        nextFactorial(N);
    }
     
}
 
// This code is contributed by AnkitRai01

Javascript




<script>
// Javascript implementation of the above approach
 
// Array that stores the factorial
// till 20
fact = Array(21).fill(0);
 
// Function to pre-compute
// the factorial till 20
function preCompute()
{
 
    // Precomputing factorials
    fact[0] = 1;
 
    for (var i = 1; i < 18; i++)
        fact[i] = (fact[i - 1] * i);
}
 
// Function to return the next
// factorial number greater than N
function nextFactorial(N)
{
    // Traverse the factorial array
    for (var i = 0; i < 21; i++) {
 
    // Find the next just greater
    // factorial than N
        if (N < fact[i]) {
 
            document.write(fact[i]);
            break;
        }
    }
}
 
// Driver Code
 
// Function to precalculate
// the factorial till 20
preCompute();
var N = 120;
 
// Function call
nextFactorial(N);
 
// This code is contributed by rutvik_56.
</script>
Output: 
720

 

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