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;
}

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.
?>

Javascript

<script>

// Javascript program to find all factorial numbers
// smaller than or equal to n.

function printFactorialNums(n)
{
    let fact = 1;
    let x = 2;
    while (fact <= n) {
        document.write(fact + " ");

        // Compute next factorial
        // using previous
        fact = fact * x;

        x++;
    }
}

// Driver code

    let n = 100;
    printFactorialNums(n);

// This code is contributed by Mayank Tyagi

</script>

Output

1 2 6 24 

Time Complexity: O(x)
Auxiliary Space: O(1)
If there are multiple queries, then we can cache all previously computed factorial numbers to avoid re-computations.
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