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How To Solve: Number and Sum of Factors of a number
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Hi All,
I have recently uploaded a video on YouTube to discuss Number and Sum of Factors of a number in Detail:
Following is covered in the video
¤ How to find Number of Factors of a number. ¤ Solved Problems: Number of Factors ¤ How to find Sum of Factors of a number. ¤ Solved Problems: Sum of Factors
How to find Number of Factors of a number.
To find number of factors of a number we need to write the number as product of power of prime number and add one to the powers and multiply the powers.
Example : Find the number of factors of 72.
72 = \(2^3 * 3^2\) => Number of factors of 72 = (3+1) * (2+1) = 4 * 3 = 12
We can list down the factors as 1 * 72 2 * 36 3 * 24 4 * 18 6 * 12 8 * 9
Solved Problems: Number of Factors
Q1 : Find number of factors of 100 and list the factors?
Sol: 100 = \(2^2 * 5^2\) => Number of factors of 100 = (2+1) * (2+1) = 3 * 3 = 9
We can list down the factors as 1 * 100 2 * 50 4 * 25 5 * 20 10 * 10
Q2 : Find number of factors of 8?
Sol: 8 = \(2^3\) => Number of factors of 8 = (3+1) = 4
We can list down the factors as 1, 2, 4, 8
How to find Sum of Factors of a number
Sum of factors of an integer n, where n = \(p^a * q^b * r^c\) (p, q, r being prime number) is given by