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Subject – Mathematics
Chapter 3 – FACTORS AND MULTIPLES

Sub-topic-4:- HCF(Highest Common Factor)

HCF of two or more numbers is the greatest number that divides each of the numbers without
leaving any remainder.
It is the greatest common factors of the given numbers.
HCF can be calculated by the following methods:
a. Factorisation Method
b. Prime Factorisation Method
c. Common Division Method

HCF by Factorisation Method
Steps to be followed:
Step 1: find all the factors of each of the given numbers
Step 2: find their common factors.
Step 3: the largest of the common factors is the HCF of the given numbers.

Example 1: find the HCF of 64 and 96.
Factors of 64 and 96 are given below:

Common factors = 1, 2, 4, 8,16 and 32.
HCF = 32
HCF by Prime Factorisation Method
We get the HCF by using the prime factors of the numbers.
We can use Factor tree method or division method to get the HCF.
Example 1: find the HCF of 24 and 60.
24 = 2 X 2 X 2 X 3
60 = 2 X 2 X 3 X 5
Product of common prime factors of 24 and 60 = 2 X 2 X 3 = 12
Hence, the HCF is 12.

HCF by Common Division Method