Page 56 - Maths Class 05
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Carry On
Complete these to show how 90 can be broken down in these particular ways.
90 90 90 90
45 18 18
2 30
3 5 5
Highest Common Factor (HCF)
The greatest factor that divides two or more numbers exactly is the Greatest Common
Divisor. We call this the Highest Common Factor (HCF).
Let us find the HCF of 30 and 45.
First, find the prime factors of each number using prime factorisation.
30 = 2 × 3 × 5 45 = 3 × 3 × 5
Next, identify those prime factors that are common in both the numbers and multiply
them. Here, both 3 and 5 are common factors. The HCF is the product of 3 and 5 i.e.,
3 × 5 = 15.
Example : Find the HCF of these pairs of numbers.
a. 15, 75 b. 14, 49
Solution : a. 15, 75
List the prime factors of each.
15 = 3 × 5
75 = 3 × 5 × 5
3 and 5 are common factors, therefore 3 × 5 = 15 is the HCF.
b. 14, 49
List the prime factors of each.
14 = 2 × 7
49 = 7 × 7
7 is common factor, therefore 7 is the HCF.
HCF has two methods to find the factors of given numbers.
« By Factorisation Method « By Division Method
Mathematics-5 56
