Prime Factorisation Method Explained with Easy Examples

Many students struggle to break numbers into simpler parts, especially when solving maths problems quickly and accurately. This is where the Prime Factorisation method becomes very useful. It helps you understand numbers deeply and solve problems in topics like HCF, LCM, and fractions.

In this blog, you will learn the prime factorisation meaning, how to do prime factorisation step by step, and how to find the prime factorisation of numbers using simple methods. We will also explore practical examples and the importance of using prime factorisation in real problems.

Let’s begin by understanding what prime factorisation really means.

What is Prime Factorisation?

The prime factorisation meaning refers to breaking down a number into a product of prime numbers only. A prime number is a number greater than 1 that has only two factors, which are 1 and itself.

For example:

• 2, 3, 5, 7, 11 are prime numbers
• 4, 6, 8 are not prime because they have more than two factors

When we express a number as a multiplication of prime numbers, we call it its product of prime factors.

Example:
12 = 2 × 2 × 3
Here, 2 and 3 are prime numbers, so this is the prime factorisation of 12.

Key points to remember:

• Every number can be expressed as a product of prime numbers
• Prime factorisation is unique for each number
• It helps simplify complex calculations

Understanding this concept builds a strong base for solving higher-level maths problems.

Prime Factorisation Method Step by Step

Now, let us understand the Prime Factorisation method in a clear and simple way. This method helps us break any number into smaller prime numbers, making calculations easier and more logical.

Method 1: Division Method

The division method is one of the most systematic and commonly used ways to find prime factors. It involves dividing the number step by step using prime numbers.

Follow these steps to find the prime factorisation:

• Start dividing the given number by the smallest prime number, which is 2
• If the number is divisible, divide it and write the result
• Continue dividing by 2 until it is no longer divisible
• Move to the next prime numbers such as 3, 5, 7, and so on
• Repeat the process until the final result becomes 1

This method ensures that you do not miss any prime factor.

Example: Find the prime factorisation of 36

• 36 ÷ 2 = 18
• 18 ÷ 2 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Now, writing all the prime numbers used in division:

36 = 2 × 2 × 3 × 3

This can also be written in exponential form as:

36 = 2² × 3²

This form is often useful in solving higher-level maths problems like HCF and LCM.

Method 2: Factor Tree Method

The factor tree method is a visual and easy-to-understand way of finding prime factors. It is especially helpful for beginners and younger students because it breaks the number step by step in a tree-like structure.

Steps to follow:

• Start by splitting the given number into any two factors
• Write those factors as branches of a tree
• Continue breaking each factor further into smaller factors
• Stop only when all the numbers at the ends of the branches are prime numbers

Example: Find the prime factorisation of 24

• 24 = 2 × 12
• 12 = 2 × 6
• 6 = 2 × 3

Now, all the final numbers are prime:

24 = 2 × 2 × 2 × 3

This method helps you clearly see how a number is broken down step by step.

Both the division method and the factor tree method give the same result. The choice of method depends on your comfort level. The division method is faster for larger numbers, while the factor tree method is easier to understand and visualize.

With regular practice, you will be able to use both methods confidently and solve problems quickly.

How to Do Prime Factorisation Easily?

If you often wonder how to do prime factorisation quickly and correctly, the key is to follow a few simple strategies and practice regularly. With the right approach, even bigger numbers become easy to solve.

Tips for Students

Here are some practical tips that can help you improve your speed and accuracy:

• Always start with the smallest prime number
  Begin dividing the number by 2, since it is the smallest prime number. This makes the process simple and organized.
• Learn divisibility rules
  Knowing rules like even numbers are divisible by 2 or numbers ending in 5 are divisible by 5 can save time and effort.
• Practice regularly with small numbers first
  Start with numbers like 10, 12, 15, and 20. Once you are comfortable, move to larger numbers.
• Use factor trees for visual learning
  Drawing a factor tree helps you clearly see how a number is broken into smaller parts, which is especially useful for beginners.

Common Mistakes to Avoid

Many students make small errors that can lead to wrong answers. Be careful of these:

• Stopping too early
  Make sure all the factors you end with are prime numbers. Do not stop when you still have a composite number.
• Missing repeated prime factors
  If a number can be divided by the same prime more than once, do not forget to include it each time.
• Confusing composite and prime numbers
  Remember that prime numbers have only two factors. Numbers like 4, 6, and 9 are not prime.

Quick Example

Let us understand this with an easy example.

Find the prime factorisation of 20

• 20 ÷ 2 = 10
• 10 ÷ 2 = 5
• 5 ÷ 5 = 1

Now, write all the prime numbers used:

20 = 2 × 2 × 5

With regular practice, you will notice that this process becomes much faster and easier. Over time, you will be able to identify prime factors almost instantly and solve problems with confidence.

Find the Prime Factorisation of Different Numbers

Let us practice how to find the prime factorisation of various numbers.

Let us understand how to break numbers step by step with some easy examples. These will help you clearly see how we find the prime factorisation and express numbers as a product of prime factors.

Example 1: 18

Start by breaking 18 into smaller factors:

• 18 = 2 × 9
• Now, 9 is not a prime number, so break it further
• 9 = 3 × 3

Now all the numbers are prime. So we write:

18 = 2 × 3 × 3

This means the prime factors of 18 are 2 and 3.

Example 2: 50

Let us break down 50 step by step:

• 50 = 2 × 25
• 25 is not a prime number, so we break it further
• 25 = 5 × 5

Now all factors are prime numbers. So:

50 = 2 × 5 × 5

This shows that 50 is made up of one 2 and two 5s.

Example 3: 72

This is a slightly bigger number, but we follow the same steps:

• 72 = 2 × 36
• 36 = 2 × 18
• 18 = 2 × 9
• 9 = 3 × 3

Now all the factors are prime numbers. So we write:

72 = 2 × 2 × 2 × 3 × 3

Or in exponential form:

72 = 2³ × 3²

Using Prime Factorisation in Maths Problems

The importance of using prime factorisation goes beyond just breaking numbers.

Applications in Maths

1. Finding HCF (Highest Common Factor)

• Write the prime factors of numbers
• Take common factors

2. Finding LCM (Least Common Multiple)

• Take the highest powers of all prime factors

3. Simplifying Fractions

• Cancel common prime factors

4. Understanding Number Properties

• Helps identify even, odd, and divisible numbers

Example: HCF of 12 and 18

12 = 2² × 3
18 = 2 × 3²

Common factors = 2 × 3 = 6

So, HCF = 6

This shows how useful prime factorisation is in solving real problems.

Prime Factorisation of Numbers in Daily Practice

Students often practice questions like prime factorisation of 1.7K or similar search queries to improve their understanding. While the number may vary, the method always remains the same.

For example, if you want to find the prime factorisation of 1700:

• 1700 = 17 × 100
• 100 = 2 × 2 × 5 × 5

So,
1700 = 2 × 2 × 5 × 5 × 17

Similarly, for the prime factorisation of 1.6K types of numbers, you follow the same steps.

Regular practice with such numbers helps build speed and accuracy.

Product of Prime Factors Explained Clearly

The product of prime factors means expressing a number as a product of prime numbers.

Example:
48 = 2 × 2 × 2 × 2 × 3

This can also be written as:
48 = 2⁴ × 3

Why is this important?

• It simplifies large calculations
• It helps in algebra and higher maths
• It improves logical thinking

Key Benefits

• Easy calculation of HCF and LCM
• Better understanding of number systems
• Useful in exams and competitive tests

PlanetSpark Maths Classes for Young Learners

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These classes are perfect for kids who find maths difficult, feel less confident while solving problems, or want to strengthen their problem-solving skills with expert support. A structured approach ensures consistent improvement and long-term academic success.

Key Features:

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• Learning through visual aids, games, and real-life examples
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• Well-structured curriculum tailored to different age groups

Practice Today, Master Tomorrow

Learning the Prime Factorisation method is not just about solving maths problems. It builds a strong foundation for logical thinking and problem-solving skills. With regular practice, even complex numbers become easy to handle.

Start with small numbers, practice daily, and gradually move to bigger ones. As your confidence grows, you will notice improvement not just in maths but also in your overall analytical ability.

Consistency is the key. Keep practicing, stay curious, and you will master this concept with ease.