Find minimum sum of factors of number - GeeksforGeeks

31 Jan, 2022
Given a number, find minimum sum of its factors.Examples:  
Input : 12
Output : 7
Explanation: 
Following are different ways to factorize 12 and
sum of factors in different ways.
12 = 12 * 1 = 12 + 1 = 13
12 = 2 * 6 = 2 + 6 = 8
12 = 3 * 4 = 3 + 4 = 7
12 = 2 * 2 * 3 = 2 + 2 + 3 = 7
Therefore minimum sum is 7

Input : 105
Output : 15
 
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++
Java
Python3
C#
PHP
Javascript
// CPP program to find minimum// sum of product of number#include <bits/stdc++.h>using namespace std; // To find minimum sum of// product of numberint 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 functionint main(){    int num = 12;     cout << findMinSum(num);     return 0;}
// 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));    }}
# Python program to find minimum# sum of product of number  # To find minimum sum of# product of numberdef 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 Codenum = 12print (findMinSum(num)) # This code is contributed by Sachin Bisht
// C# program to find minimum// sum of product of numberusing 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.
<?php// PHP program to find minimum// sum of product of number // To find minimum sum of// product of numberfunction findMinSum($num){    $sum = 0;     // Find factors of number    // and add to the sum    for ($i = 2; $i * $i <= $num; $i++)    {        while ($num % $i == 0)        {            $sum += $i;            $num /= $i;        }    }    $sum += $num;     // Return sum of numbers    // having minimum product    return $sum;} // Driver Code$num = 12; echo(findMinSum($num)); // This code is contributed by Ajit.?>
<script> // Javascript program to find minimum// sum of product of number   // To find minimum sum of// product of numberfunction findMinSum(num){    let sum = 0;       // Find factors of number    // and add to the sum    for (let 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 Codelet num = 12;   document.write(findMinSum(num));   // This code is contributed by _saurabh_jaiswal. </script>
Output: 
7
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nitin mittal
jit_t
_saurabh_jaiswal
amartyaghoshgfg
number-theory
prime-factor
Mathematical
number-theory
Mathematical
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