Here’s a typical Grade 8 Pearson Edexcel Maths Chapter 1 question, which usually focuses on Number skills, including powers and roots, multiples, factors, and prime numbers.

Question:

Find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of 36 and 60. Show your working.

Steps to solve:

1. Prime factorization of 36:
   $36 = 2^2 \times 3^2$

2. Prime factorization of 60:
   $60 = 2^2 \times 3 \times 5$

3. HCF (Highest Common Factor):
   Take the lowest powers of all common prime factors.
   $\text{HCF} = 2^2 \times 3 = 12$

4. LCM (Least Common Multiple):
   Take the highest powers of all prime factors.
   $\text{LCM} = 2^2 \times 3^2 \times 5 = 180$

Answer:

• HCF of 36 and 60 = 12
• LCM of 36 and 60 = 180

Would you like further explanation or details on any part of the solution?

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Here are 5 questions to expand your understanding:

1. What is the prime factorization of 48?
2. Can you find the HCF and LCM of 45 and 75?
3. How would you check if a number is a prime number?
4. What is the difference between the HCF and the LCM?
5. How can you use the HCF and LCM to solve problems involving fractions?

Tip: The LCM is useful when adding or subtracting fractions with different denominators.