Program to find all Factors of a Number using recursion

Last Updated : 30 Jan, 2022

Given a number N, the task is to print all the factors of N using recursion.
Examples:

Input: N = 16
Output: 1 2 4 8 16
Explanation:
1, 2, 4, 8, 16 are the factors of 16. A factor is a number which divides the number completely.
Input: N = 8
Output: 1 2 4 8

Approach: The idea is to create a function that takes 2 arguments. The function is recursively called from 1 to N and in every call, if the number is a factor of N, then it is printed. The recursion will stop when the number exceeds N.
Below is the implementation of the above approach:

C++

// C++ program to find all the factors
// of a number using recursion

#include <bits/stdc++.h>
using namespace std;

// Recursive function to
// print factors of a number
void factors(int n, int i)
{
    // Checking if the number is less than N
    if (i <= n) {
        if (n % i == 0) {
            cout << i << " ";
        }

        // Calling the function recursively
        // for the next number
        factors(n, i + 1);
    }
}

// Driver code
int main()
{
    int N = 16;
    factors(N, 1);
}

Java

// Java program to find all the factors
// of a number using recursion

class GFG {

    // Recursive function to
    // print factors of a number
    static void factors(int n, int i)
    {

        // Checking if the number is less than N
        if (i <= n) {
            if (n % i == 0) {
                System.out.print(i + " ");
            }

            // Calling the function recursively
            // for the next number
            factors(n, i + 1);
        }
    }
    // Driver code
    public static void main(String args[])
    {
        int N = 16;
        factors(N, 1);
    }
}

Python3

# Python3 program to find all the factors
# of a number using recursion

# Recursive function to
# prfactors of a number
def factors(n, i):

    # Checking if the number is less than N
    if (i <= n):
        if (n % i == 0):
            print(i, end = " ");
        
        # Calling the function recursively
        # for the next number
        factors(n, i + 1);
    
# Driver code
if __name__ == '__main__':
    N = 16;
    factors(N, 1);

# This code is contributed by Rajput-Ji

// C# program to find all the factors
// of a number using recursion

using System;

class GFG {

    // Recursive function to
    // print factors of a number
    static void factors(int n, int i)
    {

        // Checking if the number is less than N
        if (i <= n) {
            if (n % i == 0) {
                Console.WriteLine(i + " ");
            }

            // Calling the function recursively
            // for the next number
            factors(n, i + 1);
        }
    }

    // Driver code
    public static void Main()
    {
        int n = 16;
        factors(n, 1);
    }
}

JavaScript

<script>

// Javascript program to find all the factors
// of a number using recursion

// Recursive function to
// print factors of a number
function factors(n, i)
{
    // Checking if the number is less than N
    if (i <= n) {
        if (n % i == 0) {
            document.write(i + " ");
        }

        // Calling the function recursively
        // for the next number
        factors(n, i + 1);
    }
}

// Driver code
var N = 16;
factors(N, 1);

</script>

Output:

1 2 4 8 16

Time Complexity: O(N)

Auxiliary Space: O(N)

Find all factors of a Natural Number in sorted order

spp____

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Program to find all Factors of a Number using recursion

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