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

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

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; 
} 

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.

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