Number System : How to find sum and number of even and odd factors of a Number

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How to find sum and number of even and odd factors of a Number

Earlier in the article “How to find sum and number of factors of a Number” we tried to find an algorithm for sum and number of factors of a number. Now lets look into the algorithm to find out the sum and number of even and odd factors of a number. 
Algorithm
Lets take a number 720. So the question is to “Find the sum and number of even and odd Factors of 720 .”

Approach 
1. Write the number in Standard Form.
So , 720 = 2^4 x 3^2 x 5^1

2. Create  number of brackets as the number of prime factors.

3. Fill each bracket with the sum of all the powers of the respective prime number (except 2) starting from 0 to the highest power of that number,
a.) For even factors : Fill the bracket of 2 starting from 1 to the highest power of 2.
b.) For odd factors : Fill the bracket of 2 with 2^0.

Sum of the even factors  = (2^1 + 2^2 + 2^3 + 2^4) x (3^0 + 3^1 + 3^2) x (5^0 + 5^1)
= (2 + 4+ 8 +16) x (1 + 3 + 9) x (1+ 5)
= 30 x 13 x 6 = 2340

Sum of odd factors = (2^0) x (3^0 + 3^1 + 3^2) x (5^0 + 5^1)
= 1 x 13 x 6 = 78

How to find Number of even and odd factors of a Number 720?
4. Add 1 to the powers of prime factors and multiply it except for prime factor 2.
a.) For even factor : Multiply the result with power 2.
b. ) For odd factor : Multiply the result by 1.

So , 720 = 2^4 x 3^2 x 5^1
Number of even factors of 720 = (4) x(2+1) x(1+1) = 4 x 3 x 2 = 24
Number of odd factors of 720 = 1 x (2+1) x (1+1) = 3 x 2 = 6

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