The Highest Common Factor (HCF) of two numbers x and y is the highest number among all the common factors of x and y.
Example:
Find the HCF of 12 and 18.
Solution:
Factors of 12 are 1,2,3,6,12
Factors of 18 are 1,2, 3,6,9,18.
Common factors are 1,2,3,6.
So, HCF is 6.
Since this is difficult always to write all the factors especially in case of large numbers, there is a procedure to find HCF.
Finding HCF:
There are two methods to find HCF where the procedures are explained through an example.
a) Division method:
Find the HCF of 24 and 36.
Step -1: The biggest number should be divided by the small one.
Example: 36 / 24 = 1, rem 12
Step -2: Take the remainder of the first step as the divisor and the divisor of the first step as the dividend.
Example: 12 / 1 = 12, rem 0
Step-3: Repeat this step until you get zero as the remainder and the divisor of the last division is the HCF of given two numbers.
Example: Since we already have zero as the remainder the HCF is 12.
b) Factorization method:
In this method, the HCF is be found just by multiplying the common terms in the prime factorizations of the given numbers.
Example:
Find the HCF of 24 and 36.
Solution:
24 =2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
The underlined terms are common in the prime factorizations of 24 and 36.
So HCF = 2 x 2 x 3 = 12.
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