How to Find the Highest Common Factor: Prime Factor Decomposition Method

The video tutorial explains the concept of the Highest Common Factor (HCF), demonstrating how to find it using factor lists and prime factor decomposition. It provides examples with numbers 12 and 18, 27 and 90, and 48 and 180, illustrating different methods including using index form. The tutorial concludes with a recap of the methods and emphasizes the importance of following the process to accurately determine the HCF.

What is the highest common factor of 12 and 18?

• 3

• 6

• 12

• 9

Why might listing factors not be efficient for larger numbers?

• It is too quick and easy.

• It is not accurate for small numbers.

• It can be time-consuming and difficult.

• It only works for even numbers.

What is the prime factor decomposition of 27?

• 2 x 3 x 3

• 3 x 3 x 3

• 2 x 3

• 3 x 3

How do you find the HCF using prime factors in index form?

• By adding the highest powers of each prime.

• By multiplying all prime factors together.

• By subtracting the smallest prime factor.

• By identifying the lowest power of each shared prime factor.

What is the HCF of 27 and 90 using prime factor decomposition?

• 3

• 6

• 9

• 12

What is the prime factor decomposition of 48?

• 2^3 x 3

• 2^4 x 3

• 2 x 3

• 2^2 x 3

What is the HCF of 48 and 180?

• 6

• 8

• 10

• 12