Python Program for Find minimum sum of factors of number

Last Updated : 23 Jul, 2025

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

Python3

# Python program to find minimum
# sum of product of number

# To find minimum sum of
# product of number

def find_min_sum(num):
    min_sum = num
    
    for i in range(2, int(num**0.5) + 1):
        if num % i == 0:
            factor = num // i
            min_sum = min(min_sum, i + factor)
    
    return min_sum

# driver code
number = 16

# Call the function and print the result
result = find_min_sum(number)
print("The minimum sum of factors for", number, "is", result)


# This code is contributed by AYUSH MILAN

Output:

Time Complexity: O(n^1/2* log n)

Auxiliary Space: O(1)
Please refer complete article on Find minimum sum of factors of number for more details!

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