Prime Factorisation of a Number for Class 1

The reading material provided on this page for Prime Factorisation of a Number is specifically designed for students in grades 5 and 6. So, let's begin!

What is a Prime Factorisation?

Prime factorisation is the process of expressing a composite number as a product of its prime factors. This means prime factorisation is the process of finding the prime factors of a number, which are the prime numbers that can be multiplied together to give the original number.

For example, the prime factorisation of 12 is 2 x 2 x 3. Prime factorisation can be used to find the greatest common divisor (GCD) and least common multiple (LCM) of two or more numbers and simplify fractions.

Examples of Prime Factorisation

-> Prime factorisation of 16 is 2 × 2 × 2 x 2 = 24
-> Prime factorisation of 28 is 2 × 2 × 7 = 2² × 7
-> Prime factorisation of 36 is 2 × 2 × 3 × 3 = 2² × 3²
-> Prime factorisation of 42 is 2 × 3 × 7 = 2 × 3 × 7
-> Prime factorisation of 56 is 2 × 2 × 2 × 7 = 2³ × 7

Prime Factorisation Methods

The most common methods that are used for prime factorisation methods are:

1. Prime factorisation by division method
2. Prime factorisation by factor tree method

Prime Factorisation by Division Method

The division method of prime factorisation is a method of finding the prime factors of a number by dividing the number by prime numbers until the result is 1.

For example, to find the prime factorisation of 60:

Step 1: Divide 60 by 2. The result is 30.
Step 2: Divide 30 by 2. The result is 15.
Step 3: Divide 15 by 3. The result is 5.
Step 4: Divide 5 by 5. The result is 1.

The prime factorisation of 60 is 2 x 2 x 3 x 5.

This method can be used to find the prime factorisation of any number, but it is most efficient for numbers that are not prime. If the number is prime, the method will only yield the number itself as the prime factorisation.

Prime Factorisation by Tree Method

The prime factorisation tree method is a way to find the prime factorisation of a composite number. It involves breaking down the number into its prime factors by repeatedly dividing it by smaller prime numbers until only prime factors remain.

For example, to find the prime factorisation of 60 by using the prime factorisation tree method.

The prime factorisation of 60 is 2 x 2 x 3 x 5, which can be read from the tree by following the path from the top down to the bottom.

In this example, the prime factorisation tree method showed that 60 can be written as the product of the prime numbers 2, 2, 3, and 5. This method can be applied to any composite number to find its prime factorisation.

Example: Prime Factorisation of 40 using the Factor Tree Method and Division Method

Division Method

40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1

Prime factorisation: 2 × 2 × 2 × 5 = 40

Factor Tree Method

Prime factorisation: 2 × 2 × 2 × 5 = 40

Finding HCF and LCM using Prime Factorisation Method

The HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two or more numbers can be found by determining their prime factorisation.

LCM by Prime Factorisation Method

The prime factorisation method of finding the least common multiple (LCM) of two or more numbers involves breaking down each number into its prime factors and multiplying each prime factor's highest exponent (powers) together.

For example, to find the LCM of 12 and 18:

12 = 2² x 3
18 = 2 x 3²

The LCM is the product of the highest exponent (powers) of each prime factor:

LCM (12, 18) = 2² x 3² = 36
So, the LCM of 12 and 18 is 36.

NOTE: This method can also be used for finding the LCM of more than two numbers.

For example, to find the LCM of 16, 24 and 36:

16 = 2 × 2 × 2 × 2 = 2?
24 = 2 × 2 × 2 × 3 = 2³ × 3¹
36 = 2 × 2 × 3 × 3 = 2²× 3²

The LCM is the product of the highest exponent of each prime factor:

LCM (16, 24, 36) = 144

So, the LCM of 16, 24 and 36 is 144.

HCF by Prime Factorisation Method

The prime factorisation method of finding the highest common factor (HCF) of two or more numbers involves breaking down each number into its prime factors and then identifying the common prime factors and multiply the common factors with the lowest powers.

For example, to find the HCF of 24 and 36, you would first prime factorise each number: 24 = 2³ x 3 and 36 = 2² x 3².

Then, you would identify the common prime factors (2 and 3) and their lowest powers (2 and 1) and multiply those factors together to get the HCF: 2² x 3¹ = 4 x 3 = 12.