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Find all factorial numbers less than or equal to n

A number N is called a factorial number if it is the factorial of a positive integer. For example, the first few factorial numbers are

1, 2, 6, 24, 120, …

Given a number n, print all factorial numbers smaller than or equal to n.

Examples :

Input : n = 100
Output : 1 2 6 24

Input : n = 1500
Output : 1 2 6 24 120 720


A simple solution is to generate all factorials one by one until the generated factorial is greater than n.

An efficient solution is to find next factorial using previous factorial.

C++

// CPP program to find all factorial numbers
// smaller than or equal to n.
#include <iostream>
using namespace std;
  
void printFactorialNums(int n)
{
    int fact = 1;
    int x = 2;
    while (fact <= n) {
        cout << fact << " ";
  
        // Compute next factorial 
        // using previous
        fact = fact * x;
  
        x++;
    }
}
  
// Driver code
int main()
{
    int n = 100;
    printFactorialNums(n);
    return 0;
}

/div>

Java

// Java program to find all factorial numbers
// smaller than or equal to n.
  
class GFG
{
    static void printFactorialNums(int n)
    {
        int fact = 1;
        int x = 2;
        while (fact <= n)
        {
            System.out.print(fact + " ");
      
            // Compute next factorial 
            // using previous
            fact = fact * x;
      
            x++;
        }
    }
      
    // Driver code
    public static void main (String[] args) 
    {
        int n = 100;
        printFactorialNums(n);
    }
}
  
// This code is contributed by Anant Agarwal.

Python3

# Python3 program to find all factorial 
# numbers smaller than or equal to n.
  
def printFactorialNums( n):
    fact = 1
    x = 2
    while fact <= n:
        print(fact, end = " ")
          
        # Compute next factorial
        # using previous
        fact = fact * x
          
        x += 1
  
# Driver code
n = 100
printFactorialNums(n)
  
# This code is contributed by "Abhishek Sharma 44"

C#

// C# program to find all factorial numbers
// smaller than or equal to n.
using System;
  
class GFG
{
    static void printFactorialNums(int n)
    {
        int fact = 1;
        int x = 2;
        while (fact <= n)
        {
            Console.Write(fact + " ");
      
            // Compute next factorial 
            // using previous
            fact = fact * x;
      
            x++;
        }
    }
      
    // Driver code
    public static void Main () 
    {
        int n = 100;
        printFactorialNums(n);
    }
}
  
// This code is contributed by vt_m.

PHP

<?php
// PHP program to find all
// factorial numbers smaller
// than or equal to n.
  
function printFactorialNums($n)
{
    $fact = 1;
    $x = 2;
    while ($fact <= $n
    {
        echo $fact, " ";
  
        // Compute next factorial 
        // using previous
        $fact = $fact * $x;
        $x++;
    }
}
  
    // Driver code
    $n = 100;
    echo printFactorialNums($n);
  
// This code is contributed by ajit.
?>


Output:

1 2 6 24

Time Complexity : O(n)

If there are multiple queries, then we can cache all previously computed factorial numbers to avoid re-computations.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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