Find minimum sum of factors of number (original) (raw)

Last Updated : 20 Oct, 2023

Given a number N, the task is to find minimum sum of its factors.

**Examples:

**Input: 12
**Output: 7
**Explanation:
Following are different ways to factorize 12 andsum of factors in different ways.12 = 12 * 1 = 12 + 1 = 1312 = 2 * 6 = 2 + 6 = 812 = 3 * 4 = 3 + 4 = 712 = 2 * 2 * 3 = 2 + 2 + 3 = 7Therefore minimum sum is 7

**Input: 105
**Output: 15

Try It Yourself

**Approach:

To minimize sum, we must factorize factors as long as possible. With this process, we prime factors. So to find minimum sum of product of number, we find sum of prime factors of product.

C++ `

// CPP program to find minimum // sum of product of number #include <bits/stdc++.h> using namespace std;

// To find minimum sum of // product of number int findMinSum(int num) { int sum = 0;

// Find factors of number
// and add to the sum
for (int i = 2; i * i <= num; i++) {
    while (num % i == 0) {
        sum += i;
        num /= i;
    }
}
sum += num;

// Return sum of numbers
// having minimum product
return sum;

}

// Driver program to test above function int main() { int num = 12;

cout << findMinSum(num);

return 0;

}

Java

// Java program to find minimum // sum of product of number

public class Main {

// To find minimum sum of
// product of number
static int findMinSum(int num)
{
    int sum = 0;

    // Find factors of number
    // and add to the sum
    for (int i = 2; i * i <= num; i++) {
        while (num % i == 0) {
            sum += i;
            num /= i;
        }
    }
    sum += num;

    // Return sum of numbers
    // having minimum product
    return sum;
}

// Driver program to test above function
public static void main(String[] args)
{
    int num = 12;
    System.out.println(findMinSum(num));
}

}

Python3

Python program to find minimum

sum of product of number

To find minimum sum of

product of number

def findMinSum(num): sum = 0

# Find factors of number
# and add to the sum
i = 2
while(i * i <= num):
    while(num % i == 0):
        sum += i
        num //= i
    i += 1
sum += num

# Return sum of numbers
# having minimum product
return sum

Driver Code

num = 12 print (findMinSum(num))

This code is contributed by Sachin Bisht

C#

// C# program to find minimum // sum of product of number using System;

public class GFG {

// To find minimum sum of
// product of number
static int findMinSum(int num)
{
    int sum = 0;

    // Find factors of number
    // and add to the sum
    for (int i = 2; i * i <= num; i++) {
        while (num % i == 0) {
            sum += i;
            num /= i;
        }
    }
    sum += num;

    // Return sum of numbers
    // having minimum product
    return sum;
}

// Driver Code
public static void Main()
{
    int num = 12;
    Console.Write(findMinSum(num));
}

}

// This Code is contributed by Nitin Mittal.

JavaScript

PHP

`

**Output:

7

**Time Complexity : O(n1/2 * log n)
**Auxiliary Space: O(1)