What is Prime Factorisation?

S3-SA4-0030

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Prime factorisation is a way of breaking down a number into a multiplication of only prime numbers. Think of it as finding the 'building blocks' of a number using only prime numbers.

Simple Example

Quick Example

Imagine you have 12 ladoos. You want to arrange them in groups where each group has a prime number of ladoos. Prime factorisation of 12 would be 2 x 2 x 3, meaning you can arrange them in groups of 2, then 2 again, then 3 ladoos.

Worked Example

Step-by-Step

Let's find the prime factorisation of 30.
1. Start with the smallest prime number, 2. Can 30 be divided by 2? Yes.
30 ÷ 2 = 15
---2. Now we have 15. Can 15 be divided by 2? No. Move to the next smallest prime number, 3.
15 ÷ 3 = 5
---3. Now we have 5. Can 5 be divided by 3? No. Move to the next smallest prime number, 5.
5 ÷ 5 = 1
---4. We stop when we reach 1. The prime numbers we used are 2, 3, and 5.
---So, the prime factorisation of 30 is 2 x 3 x 5.

Why It Matters

Prime factorisation is super important! It's used in cryptography to keep your online chats and banking secure. Computer scientists use it in algorithms, and even economists use it to model certain patterns. It's a foundational skill for many future careers in tech and science.

Common Mistakes

MISTAKE: Using non-prime numbers in the factorisation, like 4 or 6. For example, writing 12 = 4 x 3. | CORRECTION: Always ensure all the numbers you multiply are prime numbers (numbers only divisible by 1 and themselves, like 2, 3, 5, 7...). The correct way for 12 is 2 x 2 x 3.

MISTAKE: Not fully factorising the number until all factors are prime. For example, stopping at 18 = 2 x 9. | CORRECTION: Continue breaking down composite factors (like 9) until only prime numbers remain. So, for 18, it should be 2 x 3 x 3.

MISTAKE: Missing some prime factors or repeating unnecessary steps. For example, for 24, writing 2 x 2 x 6 instead of 2 x 2 x 2 x 3. | CORRECTION: Use a systematic method like the division method (dividing by prime numbers) or a factor tree to ensure all prime factors are found and nothing is missed.

Practice Questions

Try It Yourself

QUESTION: Find the prime factorisation of 10. | ANSWER: 2 x 5

QUESTION: What is the prime factorisation of 28? | ANSWER: 2 x 2 x 7

QUESTION: A cricket team scored 36 runs in an over. Find the prime factorisation of 36. | ANSWER: 2 x 2 x 3 x 3

MCQ

Quick Quiz

Which of these is the correct prime factorisation of 24?

2 x 12

3 x 8

2 x 2 x 2 x 3

4 x 6

The Correct Answer Is:

Option C (2 x 2 x 2 x 3) correctly breaks down 24 into only prime numbers. Options A, B, and D include composite numbers (12, 8, 4, 6) which are not prime.

Real World Connection

In the Real World

When you use UPI for online payments or send messages on WhatsApp, your data is encrypted. Prime factorisation is a core idea behind this encryption. Large prime numbers are used to create codes that are very hard to break, keeping your financial transactions and personal information safe!

Key Vocabulary

Key Terms

PRIME NUMBER: A number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5, 7) | FACTOR: A number that divides another number exactly (e.g., factors of 6 are 1, 2, 3, 6) | COMPOSITE NUMBER: A number greater than 1 that has more than two factors (e.g., 4, 6, 8, 9) | FACTORISATION: Breaking down a number into a product of its factors

What's Next

What to Learn Next

Great job understanding prime factorisation! Next, you can learn about HCF (Highest Common Factor) and LCM (Lowest Common Multiple). These concepts build directly on prime factorisation and are super useful for solving many real-world problems!