Page 48 - Math Skill - 5

46 Maths

Division Method
Let us consider a number 728 and find out its prime factors using the division method.
We divide it in vertical column as shown here.

2 728 Fact-o-meter
2 364
2 182 728 = 2 × 2 × 2 × 7 × 13 To find all the prime factors of a
7 91 number, divide it successively by
13 13 prime numbers 2, 3, 5, 7, ..., etc.
1

Exercise 4.2

1. Find all the prime factors for the following numbers using factor tree method.
(a) 225 (b) 1000 (c) 256 (d) 2125 (e) 1625
2. Find all the prime factors for the following numbers using division method.
(a) 1728 (b) 61225 (c) 100000 (d) 30000 (e) 81000

3. Find the prime factors of 14 and 16 and write the prime factors which are common in both.
4. Find the prime factors of 100, 250 and 1600 and write the prime factors which are common
in all.

Highest Common Factor

The greatest number which is a common factor of two or more numbers is called their Highest
Common Factor (HCF). It is also known as the Greatest Common Divisor (GCD).
There are two methods for finding the HCF of two or more given numbers.
(a) Prime factorisation (b) Long division

Finding HCF by Prime Factorisation Method

For finding HCF by this method,

™ Find all the prime factors of the given numbers.
™ Mark all the common prime factors in the given numbers.

™ Write all common occurrences of a factor.
™ Find the product of all common factors. It gives you the required HCF.

Let’s Attempt

Example 1: Find the HCF of 18, 24 and 42 by prime factorisation method.

Solution: Prime factors of 18 = 2 × 3 × 3 2 18 2 24 2 42
Prime factors of 24 = 2 × 2 × 2 × 3 3 9 2 12 3 21

Prime factors of 42 = 2 × 3 × 7 3 3 2 6 7 7
Common prime factors = 2 × 3 1 3 3 1
Highest common factors (HCF) = 2 × 3 = 6. 1