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\\October 31, 2023 4:43 PM Bharat Arora Proof-3 Reader _________________________ Date: ___________________74

HcF aND lcM

We have learnt about the common factors and multiples in previous sections. Here,
we will learn about the Highest Common Factor (HCF) and the Lowest Common
Multiple (LCM).

Highest common Factor (HcF)
Factors of 12 Factors of 30
Let us consider the factors of 12 and 30. 5

The factors of 12 are: 1, 2, 3, 4, 6 and 12. 1 2 10
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30. 4 3 15

The common factors of 12 and 30 are: 1, 2, 3 and 6. 12 6 30
The greatest common factor among these is 6.
Common Factors
So, 6 is called the HCF of 12 and 30. of 12 and 30
Thus, the greatest common factor of all the given numbers is known as the highest

Common Factor of the numbers.
Finding HcF
Remember
We can find the HCF of given numbers using the The HCF of two or more numbers
following methods: is the highest number that can
1. By listing common factors divide all the given numbers
without leaving any remainders.
2. By prime factorisation It is also known as the Greatest
Common Divisor (GCD).
3. By common division

Let us understand these methods through examples.
Example 1: Find the HCF of 16 and 24 by listing factors.

Solution: Step 1: List the factors of all the given numbers.

The factors of 16 are: 1, 2, 4, 8 and 16.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24.

Step 2: Choose the common factors.
The common factors of 16 and 24 are: 1, 2, 4 and 8.

Step 3: Find the greatest common factor.
Here, 8 is the greatest among all these common factors.

So, the HCF of 16 and 24 is 8.

Example 2: Find the HCF of 18 and 42 by prime factorisation. 2 18 2 42
Solution: Step 1: Find the prime factorisation of given numbers. 3 9 3 21

18 = 2 × 3 × 3 and 42 = 2 × 3 × 7 3 7
Step 2: Look at the prime factors which are common in both. They are 2
and 3.

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