Page 162 - New Medley 5 Semester 1

Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 12
Factors of 20
Factors of 20: 1, 2, 4, 5, 10, 20

3 5
Common factors of 12 and 20 are 1, 2

and 4. 6 10
1
The highest common factor of 12 and 20 12 4 2 20

is 4.
Common factors of 12 and 20
Thus, the Highest Common Factor (HCF)

is the greatest number that divides the two or more given numbers
completely without leaving any remainder. Sometimes, the HCF is also

called GCD (Greatest Common Divisor). There are three ways to find the
HCF of the given numbers.

I. By using factor and common factor method

II. By prime factorisation method

III. By continued division method

Let us understand these methods through examples.

Example 3: Find the HCF of 24 and 40.
Solution: Method I

Factors of 24 = 1 , 2 , 3, 4 , 6, 8 , 12, 24

Factors of 40 = 1 , 2 , 4 , 5, 8 , 10, 20, 40

Common factors of 24 and 40 = 1, 2, 4, 8

∴ The HCF of 24 and 40 = 8

Method II
224 240

212 220

2 6 210
3 3 5 5

1 1

∴ 24 = 2 × 2 × 2 × 3 ∴ 40 = 2 × 2 × 2 × 5

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