What is Prime Factorisation Method for HCF?

S3-SA4-0033

Grade Level:

Class 6

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

Definition

What is it?

The Prime Factorisation Method for HCF (Highest Common Factor) is a way to find the largest number that divides two or more numbers exactly, using their prime factors. We break down each number into its prime factors and then find the common ones.

Simple Example

Quick Example

Imagine you have 12 ladoos and 18 jalebis. You want to arrange them into identical plates, with each plate having the same number of ladoos and jalebis, and no sweets left over. To find the maximum number of plates you can make, you need to find the HCF of 12 and 18 using prime factorisation.

Worked Example

Step-by-Step

Let's find the HCF of 24 and 36 using the Prime Factorisation Method.

Step 1: Find the prime factors of 24.
24 = 2 x 12
12 = 2 x 6
6 = 2 x 3
So, 24 = 2 x 2 x 2 x 3

---

Step 2: Find the prime factors of 36.
36 = 2 x 18
18 = 2 x 9
9 = 3 x 3
So, 36 = 2 x 2 x 3 x 3

---

Step 3: Identify the common prime factors from both lists.
For 24: (2 x 2 x 2 x 3)
For 36: (2 x 2 x 3 x 3)
Common factors are: 2, 2, 3

---

Step 4: Multiply the common prime factors to find the HCF.
HCF = 2 x 2 x 3 = 12

---

Answer: The HCF of 24 and 36 is 12.

Why It Matters

Understanding HCF helps in many fields! Engineers use it when designing circuits or arranging components efficiently. Computer scientists use it in algorithms for data encryption, which keeps your online messages safe. Even in AI, it helps in optimizing processes.

Common Mistakes

MISTAKE: Listing all factors instead of only prime factors. | CORRECTION: Always break numbers down until you only have prime numbers (like 2, 3, 5, 7, 11...).

MISTAKE: Forgetting to multiply all common prime factors. | CORRECTION: After identifying all common prime factors, make sure to multiply them together to get the final HCF.

MISTAKE: Including non-common factors in the HCF calculation. | CORRECTION: Only select the prime factors that are present in the factorisation of ALL the numbers you are finding the HCF for.

Practice Questions

Try It Yourself

QUESTION: Find the HCF of 10 and 15 using prime factorisation. | ANSWER: 5

QUESTION: What is the HCF of 28 and 42? | ANSWER: 14

QUESTION: A class has 30 boys and 45 girls. The teacher wants to divide them into groups so that each group has the same number of boys and the same number of girls, with no students left over. What is the largest number of groups possible? | ANSWER: 15

MCQ

Quick Quiz

What are the common prime factors of 12 and 20?

2, 3

2, 2

2, 5

3, 5

The Correct Answer Is:

Prime factors of 12 are 2 x 2 x 3. Prime factors of 20 are 2 x 2 x 5. The common prime factors are two 2s.

Real World Connection

In the Real World

When you buy tiles for your home, say you have a room that is 12 feet by 18 feet. To cover the floor with the largest possible square tiles without cutting any, you'd find the HCF of 12 and 18. This helps workers at construction sites calculate materials efficiently, saving money and reducing waste.

Key Vocabulary

Key Terms

PRIME NUMBER: A number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5) | FACTOR: A number that divides another number exactly without leaving a remainder | PRIME FACTORISATION: Breaking down a number into a product of its prime factors | HCF (HIGHEST COMMON FACTOR): The largest number that divides two or more numbers exactly

What's Next

What to Learn Next

Great job understanding HCF! Next, you should explore the 'Least Common Multiple (LCM) using Prime Factorisation'. It's another important concept that builds on prime factors and helps solve different kinds of real-world problems.