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# Print all combinations of factors (Ways to factorize)

• Difficulty Level : Hard
• Last Updated : 23 Jun, 2022

Write a program to print all the combinations of factors of given number n.

Examples:

```Input : 16
Output :2 2 2 2
2 2 4
2 8
4 4

Input : 12
Output : 2 2 3
2 6
3 4```

To solve this problem we take one array of array of integers or list of list of integers to store all the factors combination possible for the given n. So, to achieve this we can have one recursive function which can store the factors combination in each of its iteration. And each of those list should be stored in the final result list.

Below is the implementation of the above approach.

Output

```2 2 2 2
2 2 4
2 8
4 4 ```

#### Another Approach:

The code below is pure recursive code for printing all combinations of factors:

It uses a vector of integer to store a single list of factors and a vector of integer to store all combinations of factors. Instead of using an iterative loop, it uses the same recursive function to calculate all factor combinations.

## C++

 `// C++ program to print all factors combination` `#include ` `using` `namespace` `std;`   `// vector of vector for storing` `// list of factor combinations` `vector > factors_combination;`   `// recursive function` `void` `compute_factors(``int` `current_no, ``int` `n, ``int` `product,` `                     ``vector<``int``> single_list)` `{` `    `  `    ``// base case: if the product ` `    ``// exceeds our given number;` `    ``// OR` `    ``// current_no exceeds half the given n` `    ``if` `(current_no > (n / 2) || product > n)` `        ``return``;`   `    ``// if current list of factors` `    ``// is contributing to n` `    ``if` `(product == n) {` `      `  `        ``// storing the list` `        ``factors_combination.push_back(single_list); ` `      `  `        ``// into factors_combination` `        ``return``; ` `    ``}`   `    ``// including current_no in our list` `    ``single_list.push_back(current_no); `   `    ``// trying to get required ` `    ``// n with including current` `    ``// current_no` `    ``compute_factors(current_no, n, product * current_no,` `                    ``single_list);`   `    ``// excluding current_no from our list` `    ``single_list.pop_back(); `   `    ``// trying to get required n ` `    ``// without including current` `    ``// current_no` `    ``compute_factors(current_no + 1, n, product,` `                    ``single_list);` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `n = 16;`   `    ``// vector to store single list of factors` `    ``// eg. 2,2,2,2 is one of the list for n=16` `    ``vector<``int``> single_list;`   `    ``// compute_factors ( starting_no, given_n,` `    ``// our_current_product, vector )` `    ``compute_factors(2, n, 1, single_list);`   `    ``// printing all possible factors stored in` `    ``// factors_combination` `    ``for` `(``int` `i = 0; i < factors_combination.size(); i++) {` `        ``for` `(``int` `j = 0; j < factors_combination[i].size();` `             ``j++)` `            ``cout << factors_combination[i][j] << ``" "``;` `        ``cout << endl;` `    ``}` `    ``return` `0;` `}`   `// code contributed by Devendra Kolhe`

## Java

 `// Java program to print all factors combination` `import` `java.util.*;`   `class` `GFG{` `    `  `// vector of vector for storing` `// list of factor combinations` `static` `Vector> factors_combination = ` `   ``new` `Vector>();` ` `  `// Recursive function` `static` `void` `compute_factors(``int` `current_no, ``int` `n, ``int` `product,` `                            ``Vector single_list)` `{` `      `  `    ``// base case: if the product` `    ``// exceeds our given number;` `    ``// OR` `    ``// current_no exceeds half the given n` `    ``if` `(current_no > (n / ``2``) || product > n)` `        ``return``;` `  `  `    ``// If current list of factors` `    ``// is contributing to n` `    ``if` `(product == n) ` `    ``{` `        `  `        ``// Storing the list` `        ``factors_combination.add(single_list);` `        `  `        ``// Printing all possible factors stored in` `        ``// factors_combination` `        ``for``(``int` `i = ``0``; i < factors_combination.size(); i++)` `        ``{` `            ``for``(``int` `j = ``0``; j < factors_combination.get(i).size(); j++)` `                ``System.out.print(factors_combination.get(i).get(j) + ``" "``);` `        ``}` `        ``System.out.println();` `        ``factors_combination = ``new` `Vector>();` `        `  `        ``// Into factors_combination` `        ``return``;` `    ``}` `  `  `    ``// Including current_no in our list` `    ``single_list.add(current_no);` `  `  `    ``// Trying to get required` `    ``// n with including current` `    ``// current_no` `    ``compute_factors(current_no, n, ` `                    ``product * current_no,` `                    ``single_list);` `  `  `    ``// Excluding current_no from our list` `    ``single_list.remove(single_list.size() - ``1``);` `  `  `    ``// Trying to get required n` `    ``// without including current` `    ``// current_no` `    ``compute_factors(current_no + ``1``, n, product, ` `                    ``single_list);` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `n = ``16``;`   `    ``// Vector to store single list of factors` `    ``// eg. 2,2,2,2 is one of the list for n=16` `    ``Vector single_list = ``new` `Vector();` `  `  `    ``// compute_factors ( starting_no, given_n,` `    ``// our_current_product, vector )` `    ``compute_factors(``2``, n, ``1``, single_list);` `}` `}`   `// This code is contributed by decode2207`

## Python3

 `# Python3 program to print all factors combination`   `# vector of vector for storing` `# list of factor combinations` `factors_combination ``=` `[]`   `# recursive function` `def` `compute_factors(current_no, n, product, single_list):` `    ``global` `factors_combination` `    `  `    ``# base case: if the product` `    ``# exceeds our given number;` `    ``# OR` `    ``# current_no exceeds half the given n` `    ``if` `((current_no > ``int``(n ``/` `2``)) ``or` `(product > n)):` `        ``return` ` `  `    ``# if current list of factors` `    ``# is contributing to n` `    ``if` `(product ``=``=` `n):` `        ``# storing the list` `        ``factors_combination.append(single_list)` `        `  `        ``# printing all possible factors stored in` `        ``# factors_combination` `        ``for` `i ``in` `range``(``len``(factors_combination)):` `            ``for` `j ``in` `range``(``len``(factors_combination[i])):` `                ``print``(factors_combination[i][j], end``=``" "``)` `        ``print``()` `        ``factors_combination ``=` `[]` `        ``# into factors_combination` `        ``return` ` `  `    ``# including current_no in our list` `    ``single_list.append(current_no)` ` `  `    ``# trying to get required` `    ``# n with including current` `    ``# current_no` `    ``compute_factors(current_no, n, product ``*` `current_no, single_list)` ` `  `    ``# excluding current_no from our list` `    ``single_list.pop()` ` `  `    ``# trying to get required n` `    ``# without including current` `    ``# current_no` `    ``compute_factors(current_no ``+` `1``, n, product, single_list)`   `n ``=` `16`   `# vector to store single list of factors` `# eg. 2,2,2,2 is one of the list for n=16` `single_list ``=` `[]`   `# compute_factors ( starting_no, given_n,` `# our_current_product, vector )` `compute_factors(``2``, n, ``1``, single_list)`   `# This code is contributed by ukasp.`

## C#

 `// C# program to print all factors combination` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG {` `    `  `    ``// vector of vector for storing` `    ``// list of factor combinations` `    ``static` `List> factors_combination = ``new` `List>();` `    `  `    ``// recursive function` `    ``static` `void` `compute_factors(``int` `current_no, ``int` `n, ``int` `product, List<``int``> single_list)` `    ``{` `         `  `        ``// base case: if the product` `        ``// exceeds our given number;` `        ``// OR` `        ``// current_no exceeds half the given n` `        ``if` `(current_no > (n / 2) || product > n)` `            ``return``;` `     `  `        ``// if current list of factors` `        ``// is contributing to n` `        ``if` `(product == n) {` `            `  `            ``// storing the list` `            ``factors_combination.Add(single_list);` `            ``// printing all possible factors stored in` `            ``// factors_combination` `            ``for``(``int` `i = 0; i < factors_combination.Count; i++)` `            ``{` `                ``for``(``int` `j = 0; j < factors_combination[i].Count; j++)` `                ``Console.Write(factors_combination[i][j] + ``" "``);` `            ``}` `            ``Console.WriteLine();` `            ``factors_combination = ``new` `List>();` `            ``// into factors_combination` `            ``return``;` `        ``}` `     `  `        ``// including current_no in our list` `        ``single_list.Add(current_no);` `     `  `        ``// trying to get required` `        ``// n with including current` `        ``// current_no` `        ``compute_factors(current_no, n, product * current_no, single_list);` `     `  `        ``// excluding current_no from our list` `        ``single_list.RemoveAt(single_list.Count - 1);` `     `  `        ``// trying to get required n` `        ``// without including current` `        ``// current_no` `        ``compute_factors(current_no + 1, n, product, single_list);` `    ``}`   `  ``static` `void` `Main() {` `    ``int` `n = 16;` ` `  `    ``// vector to store single list of factors` `    ``// eg. 2,2,2,2 is one of the list for n=16` `    ``List<``int``> single_list = ``new` `List<``int``>();` ` `  `    ``// compute_factors ( starting_no, given_n,` `    ``// our_current_product, vector )` `    ``compute_factors(2, n, 1, single_list);` `  ``}` `}`   `// This code is contributed by divyesh072019.`

## Javascript

 ``

Output

```2 2 2 2
2 2 4
2 8
4 4 ```

Time Complexity: O(n2) , n is the size of vector
Auxiliary Space: O(n2), n is the size of vector

Please suggest if someone has a better solution which is more efficient in terms of space and time.