Find minimum sum of factors of number
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 7Input: 105
Output: 15
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
<script> // Javascript program to find minimum // sum of product of number // To find minimum sum of // product of number function 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 Code let num = 12; document.write(findMinSum(num)); // This code is contributed by _saurabh_jaiswal. </script> |
PHP
<?php // PHP program to find minimum // sum of product of number // To find minimum sum of // product of number function 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. ?> |
Output:
7
Time Complexity : O(n1/2 * log n)
Auxiliary Space: O(1)