Maximize the product of four factors of a Number in C++

Given the task is to calculate the maximum product that can be obtained from four factors A, B, C, D of a given number N, given the condition −

The sum of the four factors should be equal to the number N, that is, N=A+B+C+D.

Input − N=10

Output − 20

Explanation − The factors of 10 are: 1, 2, 5, 10.

Maximum product can be obtained by multiplying 5*2*2*1=20 and also it satisfies the given condition, that is, 5+2+2+1=10.

Input − N=16

Output − 256

Explanation − The factors of 16 are: 1, 2, 4, 8, 16.

Maximum product can be obtained by multiplying 4*4*4*4=256 and also it satisfies the given condition, that is, 4+4+4+4=16.

Approach used in the below program as follows

• Create an array Factors[] of type int to store the factors of given number and a variable K=0 of type int to keep track of the size of array occupied .

• Create a function FindFactors() to find the factors of given numbers.

• Loop from i=1; i*i<=N; i++

• Inside the loop set if (N%i == 0) to check if I is a factor or not.

• If i is a factor, then check if (N/I == i). If yes then insert i into the Factors[] else pass both N/i and i into Factors[].

• Create function Product() to find the maximum product out of the factors.

• Initialize int product=0; and size=K+1;

• Initialize four new nested loops and run them till ‘size’.

• Inside the loops, initialize int sum= Factors[i] + Factors[] + Factors[k] + Factors[l];

• Check if (sum == N) and if so then initialize pro=Factors[i] * Factors[j] * Factors[k] * Factors[l];

• Then check if (pro > product), if so then put product=pro;

• return product

Example

 Live Demo

#include <bits/stdc++.h> using namespace std; //Array to store the factors int Factors[30]; int K=0; //Function to find out the factors int FindFactors(int N){    //Looping until i reaches the sqrt(N)    for (int i = 1; i * i <= N; i++){       if (N % i == 0){          /* if both the factors are same then only one will be inserted*/          if ((N / i) == i){             Factors[K]=i;             K++;          }          else{             //Inserting 1st factor in array             Factors[K]=N/i;             K++;             //Inserting 2st factor in array             Factors[K]=i;             K++;          }       }    } } // Function to find the maximum product int Product(int N){    int product = 0;    int size = K+1;    for (int i = 0; i < size; i++)       for (int j = 0; j < size; j++)          for (int k = 0; k < size; k++)             for (int l = 0; l < size; l++){                //Adding each set of factors                int sum = Factors[i] + Factors[j] + Factors[k] + Factors[l];                //Checking if the sum is equal to N                if (sum == N){                   //Multiplying the factors                   int pro = Factors[i] * Factors[j] * Factors[k] * Factors[l];                   //Replacing the value of product if a larger value is found                   if(pro > product)                      product = pro;                }             }    return product; } //Main function int main(){    int N = 10;    //Calling function to find factors of N    FindFactors(N);    //Calling function to find the maximum product    cout<<Product(N);    return 0; }

Output

If we run the above code we will get the following output −

Maximum Profit: 20