Prime Factorisation: Methods, Steps and Examples for Class 6

Prime factorisation is a method of breaking down a number into its smallest prime factors. It helps break down complex numbers into simpler building blocks, making calculations easier and more systematic. This concept is widely used in solving problems related to factors and multiples. In this topic, you will learn how to find the prime factorisation of numbers using simple methods like division and factor trees with clear explanations and examples for better understanding.

Table of Contents

• What is Prime Factorisation?
• The Factor Tree Method
• The Division Method (Ladder Method)
• Writing Prime Factorisation in Exponent Form
• Using Prime Factorisation to Find LCM and HCF
• Solved Examples of Prime Factorisation for Class 6
• Practice Questions of Prime Factorisation for Class 6

What is Prime Factorisation?

Expressing a number as a product of its factors is called factorisation.

Every whole number greater than 1 is either a prime number or can be broken down into a set of smaller prime numbers multiplied together. This process of ‘breaking a number down to its prime building blocks’ is called prime factorisation. Any composite number can be expressed as a product of its factors. Expressing a number as the product of its prime factors is called prime factorisation.

Example: 12 = 2 × 2 × 3, 30 = 2 × 3 × 5, 48 = 2 × 2 × 2 × 2 × 3

The Factor Tree Method

The factor tree method is the most visual method of prime factorisation.

How to Draw a Factor Tree: 

• Write the number at the top.

• Split it into any two factors (not 1 and the number itself). Draw two branches going down.

• Check each factor: if it's a prime, circle it (it's a leaf). If it's composite, split it again.

• Repeat until every branch ends in a prime (circled leaf).

• Collect all the circled primes and write them as a multiplication. That is your prime factorisation.

Example: Factorisation of the number 12 is given below

The prime factorisation of 12 is 3 × 2 × 2.

From the above example, we can see that the prime factorisation of any number is unique. 

The Division Method (Ladder Method)

The division method, also called the 'ladder method' or 'continuous division method', is the standard method to find the prime factorisation of any number.

How to Use the Division Method:

• Write the number on the right side of a small ‘L’ shape (like a division bracket).

• Find the smallest prime number that divides your number exactly (with no remainder). Write that prime on the left.

• Write the quotient (result of dividing) below.

• Repeat with the new quotient again: divide by the smallest prime that goes in exactly.

• Stop when the quotient is 1. All the primes on the left are the prime factors.

Example: Determine the prime factorisation of 36.

 

The prime factorisation of 36 is 2 × 2 × 3 × 3.

Writing Prime Factorisation in Exponent Form

Prime factorisation can be written in exponent form by expressing repeated prime factors as powers. Instead of writing the same factor multiple times, we use exponents to make the expression shorter 

For example, if 24 is written as 2 × 2 × 2 × 3, it can be expressed in exponent form as 2³ × 3, where 3 is the exponent indicating how many times 2 is multiplied.

 

Using Prime Factorisation to Find LCM and HCF

Prime factorisation gives the most reliable way to find the LCM and HCF of any two or more numbers.

HCF (Highest Common Factor)

The HCF is the largest number that divides all the given numbers exactly. Using prime factorisation: take the product of the common prime factors with their lowest exponents.

Example: Find the HCF of 36 and 60

36 = 2² × 3²

60 = 2² × 3 × 5

Common primes: 2 (lowest power = 2²) and 3 (lowest power = 3¹)

HCF = 2² × 3 = 4 × 3 = 12

HCF(36, 60) = 12

LCM (Lowest Common Multiple)

The LCM is the smallest number that is a multiple of all the given numbers. Using prime factorisation: take the product of all prime factors with their highest exponents.

Example: Find the LCM of 36 and 60

36 = 2² × 3²

60 = 2² × 3 × 5

All primes, highest powers: 2² × 3² × 5

LCM = 4 × 9 × 5 = 180

LCM(36, 60) = 180

Solved Examples of Prime Factorisation for Class 6

Example 1: Find the prime factorisation of 48 using the factor tree method.

Solution: 

 

Example 2: Find the prime factorisation of 72 using the division method

Solution:  27223621839331

Therefore, the prime factorisation of 72 = 2 × 2 × 2 × 3 × 3.

Example 3: Find the prime factorisation of 50

Solution:  250525551

Therefore, the prime factorisation of 50 = 2 × 5 × 5

Example 4: Find the HCF and LCM of 48 and 72 using prime factorisation.

Solution: 48=24×3 and 72=23×32

HCF (Highest Common Factor)

Take the smallest powers of common primes: HCF = 23 × 3 = 8 × 3 = 24

LCM (Least Common Multiple)

Take the highest powers of all primes: LCM=24 × 32

= 16 × 9 = 144

HCF=24, LCM=144

Example 5: Find the prime factors of 252.

Solution:  22522126363321771

Therefore, the prime factorisation of 252 = 2 × 2 × 3 × 3 × 7 = 2² × 3² × 7.

Practice Questions of Prime Factorisation for Class 6

1. Find the prime factorisation of 53.

2. Find the prime factorisation of 56 using the division method.

3. Draw a factor tree for 120 and write its prime factorisation.

4. Find the prime factorisation of 90 using a factor tree.

5. Find the prime factorisation of 24 using the division method.

6. Find the HCF and LCM of 12, 15 and 21 using prime factorisation.

7. A school has 84 boys and 120 girls. The teacher wants to form equal groups with the maximum number of students in each group, with no student left over. Find the maximum group size using prime factorisation. (Hint: Find HCF)

8. Find the HCF and LCM of 36 and 48 using prime factorisation.

9. Find the prime factorisation of 45 using a factor tree.

10. Find the HCF and LCM of 38 and 30 using prime factorisation.