Python Program for Find sum of even factors of a number
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 sum 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
import math
def sumofFactors(n) :
if (n % 2 ! = 0 ) :
return 0
res = 1
for i in range ( 2 , ( int )(math.sqrt(n)) + 1 ) :
count = 0
curr_sum = 1
curr_term = 1
while (n % i = = 0 ) :
count = count + 1
n = n / / i
if (i = = 2 and count = = 1 ) :
curr_sum = 0
curr_term = curr_term * i
curr_sum = curr_sum + curr_term
res = res * curr_sum
if (n > = 2 ) :
res = res * ( 1 + n)
return res
n = 18
print (sumofFactors(n))
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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
def evenfactorssum(n):
s = 0
for i in range ( 1 , n + 1 ):
if n % i = = 0 :
if i % 2 = = 0 :
s = s + i
print (s)
n = 18
evenfactorssum(n)
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Method: Using the list comprehension
Python3
n = 18
x = [i for i in range ( 1 ,n + 1 ) if n % i = = 0 and i % 2 = = 0 ]
print ( sum (x))
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Time Complexity: O(n), where n is length of x list.
Auxiliary Space: O(n), where n is number of elements in list x.
Method: Using lambda function
Python3
n = 18
l = [i for i in range ( 1 , n + 1 ) if n % i = = 0 ]
s = list ( filter ( lambda x: (x % 2 = = 0 ), l))
print ( sum (s))
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Method: Using enumerate function
Python3
n = 18
x = [ str (i) for i in range ( 1 ,n + 1 )]
s = [ int (i) for i in x if n % int (i) = = 0 and int (i) % 2 = = 0 ]
print ( sum (s))
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Please refer complete article on Find sum of even factors of a number for more details!
Last Updated :
08 May, 2023
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