# Factor Combinations in C++

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Suppose we have a number. The numbers can be regarded as a product of its factors. So, 8 = 2 x 2 x 2; = 2 x 4. We have to make one function that takes an integer n and return all possible combinations of its factors.

So, if the input is like 12, then the output will be [[2, 6], [2, 2, 3], [3, 4]]

To solve this, we will follow these steps −

• Define a function solve(), this will take n, target, start,

• define one list of lists called ret

• if n is same as 1, then −

• return ret

• if n is not equal to target, then −

• insert n at the end of ret

• for initialize i := start, when i * i <= n, update (increase i by 1), do −

• if n mod i is same as 0, then −

• other = solve(n / i, target, i)

• for initialize j := 0, when j < size of other, update (increase j by 1), do −

• insert i at the end of other[j]

• insert other[j] at the end of ret

• return ret

• From the main method do the following −

• return solve(n, n, 2)

## Example

Let us see the following implementation to get a better understanding −

Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<vector<auto< > v){
cout << "[";
for(int i = 0; i<v.size(); i++){
cout << "[";
for(int j = 0; j <v[i].size(); j++){
cout << v[i][j] << ", ";
}
cout << "],";
}
cout << "]"<<endl;
}
class Solution {
public:
vector < vector <int< > solve(int n, int target, int start){
vector < vector <int< > ret;
if(n == 1){
return ret;
}
if(n != target){
ret.push_back({n});
}
for(int i = start; i * i <= n; i++){
if(n % i == 0){
vector < vector <int< > other = solve(n / i, target,i);
for(int j = 0; j < other.size(); j++){
other[j].push_back(i);
ret.push_back(other[j]);
}
}
}
return ret;
}
vector<vector<int<> getFactors(int n) {
return solve(n, n, 2);
}
};
main(){
Solution ob;
print_vector(ob.getFactors(16));
}

## Input

16

## Output

[[8, 2, ],[4, 2, 2, ],[2, 2, 2, 2, ],[4, 4, ],]