Page 54 - Start Up Mathematics_5

EXERCISE 3.2

1. Which of the following pairs are co-prime?
(a) 16 and 21 (b) 18 and 35 (c) 24 and 39 (d) 46 and 108 (e) 55 and 57

2. Sort the prime, composite and all pairs of co-prime numbers from the table.

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Highest Common Factor (HCF)

Let’s find all the factors of 24 and 32.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Factors of 32 are 1, 2, 4, 8, 16 and 32.

Common factors of 24 and 32 are 1, 2, 4 and 8.
Out of these the highest common factor is 8, i.e., 8 is the greatest number which divides 24
and 32 without leaving a remainder.

So, we say that the Highest Common Factor (HCF) of 24 and 32 is 8.

HCF is also known as the Greatest Common Divisor (GCD). Thus, HCF (or GCD) of two or
more numbers is defined as the greatest number that exactly divides all the given numbers
without leaving a remainder.
To find the HCF of two or more numbers, we can use two methods.

1. Prime factorization 2. Long division method

HCF by prime factorization

We know how to write a number as a product of its prime factors. Let’s learn to use it to
find HCF.

Example 11: Find the HCF of 15 and 20 using prime factorization.
Solution: Prime factors of 15 = 3 × 5 3 15 2 20

Prime factors of 20 = 2 × 2 × 5 5 5 2 10
15 = 3 × 5 1 5 5
Common prime factor 1
20 = 2 × 2 × 5
The product of common prime factors is the HCF.
So, the HCF of 15 and 20 is 5.

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