Python Program for Find sum of even factors of a number

08 Jun, 2022
Given a number n, the task is to find the even factor sum of a number. Examples:
Input : 30
Output : 48
Even dividers sum 2 + 6 + 10 + 30 = 48

Input : 18
Output : 26
Even dividers sum 2 + 6 + 18 = 26
Let p1, p2, ... pk be prime factors of n. Let a1, a2, .. ak be highest powers of p1, p2, .. pk respectively that divide n, i.e., we can write n as n = (p1a1)*(p2a2)* ... (pkak).
Sum of divisors = (1 + p1 + p12 ... p1a1) * 
                  (1 + p2 + p22 ... p2a2) *
                  ...........................
                  (1 + pk + pk2 ... pkak) 
If number is odd, then there are no even factors, so we simply return 0. If number is even, we use above formula. We only need to ignore 20. All other terms multiply to produce even factor sum. For example, consider n = 18. It can be written as 2132 and sun of all factors is (20 + 21)*(30 + 31 + 32). if we remove 20 then we get the Sum of even factors (2)*(1+3+32) = 26. To remove odd number in even factor, we ignore then 20 which is 1. After this step, we only get even factors. Note that 2 is the only even prime. 
python3
# Formula based Python3# program to find sum# of alldivisors of n.import math # Returns sum of all# factors of n.def sumofFactors(n) :         # If n is odd, then    # there are no even    # factors.    if (n % 2 != 0) :        return 0      # Traversing through    # all prime factors.    res = 1    for i in range(2, (int)(math.sqrt(n)) + 1) :                 # While i divides n        # print i and divide n        count = 0        curr_sum = 1        curr_term = 1        while (n % i == 0) :            count= count + 1              n = n // i              # here we remove the            # 2^0 that is 1. All            # other factors            if (i == 2 and count == 1) :                curr_sum = 0              curr_term = curr_term * i            curr_sum = curr_sum + curr_term                 res = res * curr_sum               # This condition is to    # handle the case when    # n is a prime number.    if (n >= 2) :        res = res * (1 + n)      return res  # Driver coden = 18print(sumofFactors(n))  # This code is contributed by Nikita Tiwari.
26

Method: Finding even factors sum of a given number using only for loop and if statements .
1. Iterate from the start range 1 to the given number to find the factors of a number using modulo division.
2. Finding even factors from the obtained factors by performing modulo division of a factor with 2. if the result of modulo division is equal to 0 then it should be considered as an even factor.
3. Adding all even factors and storing the result in s.
4. Print the sum of the even factors. 
Python3
# Python code# To find the sum of even factors of a number  def evenfactorssum(n):    s = 0    for i in range(1, n+1):        # finding factors of a given number        if n % i == 0:            # finding even factors of a given number            if i % 2 == 0:                # adding even factors of a given number                s = s+i  # 2+6+10+30                # printing the sum of even factors of a given number    print(s)  # driver code# inputn = 18# the above input can also be given as# n=int(input()) -> taking input from the userevenfactorssum(n) # this code is contributed by gangarajula laxmi
26

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