# 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**

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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.

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**Algorithm **

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**Lets take a number 720. So the question is to “Find the sum and number of even and odd Factors of 720 .”**

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**Approach **

*1.Write the number in Standard Form.*

So , 720 = 2^4 x 3^2 x 5^1

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*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

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**How to find Number of even and odd factors of a Number 720?**

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*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.

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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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