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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) 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.

Step 2: List the factors of the second number, that is, 30.

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
Step 3: List the common factors of both the 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 (c) 70, 105 and 175

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 prime common 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 (c) 70, 105, 175 2 70 3 105 5 175
3 9 3 21 5 35 5 35 5 35
3 3 7 7 7 7 7 7 7 7
1 1 1 1 1
27 = 3 × 3 × 3, 63 = 3 × 3 × 7 70 = 2 × 5 × 7 105 = 3 × 5 × 7

175 = 5 × 5 × 7

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