Page 71 - MathGPT_V1.0_C5

D:\Surender Prajapati\Books Final_CBSE and ICSE\ICSE\Preparatory_Stage_Maths-5_(31-10-2023)\Open_Files\CHAP_03
\\November 3, 2023 11:27 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Methods of Finding HCF

We can find the HCF of two or more numbers by any of the three methods:

(i) Common factors method (ii) Prime factorisation method

(iii) Common division method (iv) Long division method

Common Factors Method

Example 1: Find the HCF of 12 and 30 using the common factor method.
Solution: Step 1: List the factors of the first number, that is, 12.

Factors of 12 are 1, 2, 3, 4, 6 and 12. Note
The HCF of two
Step 2: List the factors of the second number, that is, 30. or more numbers

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. cannot be bigger
than any one
Step 3: List the common factors of both the numbers. of the given
numbers.
Common factors of 12 and 30 are 1, 2, 3 and 6.
Step 4: Choose the highest common factor, that is, 6.

Thus, the highest common factor (HCF) of 12 and 30 is 6.

Prime Factorisation Method

Step 1: Express each number as a product of its prime factors.

Step 2: Find the factors common to all the numbers given.
Step 3: The product of these numbers is the HCF of the given number.

Example 2: Find HCF of the following numbers by using the prime factorisation method:

(a) 24 and 36 (b) 27 and 63
Solution:

(a) 2 24 2 36

2 12 2 18 Remember
2 6 3 9 The HCF of two or more
3 3 3 3 numbers is the product of
1 1 their common prime factors.

24 = 2 × 2 × 2 × 3 36 = 2 × 2 × 3 × 3
The common factors of 24 and 36 are 2, 2 and 3
HCF of 24 and 36 = 2 × 2 × 3 = 12

(b) 27, 63 3 27 3 63
3 9 3 21
3 3 7 7 Common factors of 27 and 63 are 3 and
1 1 3. Thus, the HCF of 27 and 63 = 3 × 3
27 = 3 × 3 × 3, 63 = 3 × 3 × 7 = 9.

Mathematics-5 69