Factors and Multiples

Summary and Exam Tips for Factors and Multiples

Factors and Multiples is a subtopic of Number, which falls under the subject Mathematics in the Edexcel Lower Secondary curriculum. Multiples of a number are the results of multiplying that number by integers. For example, the multiples of 3 are 3, 6, 9, 12, etc. Common multiples are numbers that are multiples of two or more numbers, such as 12, 24, and 36 for 3 and 4. The lowest common multiple (LCM) is the smallest common multiple shared by two or more numbers. For instance, the LCM of 4 and 5 is 20.

Factors are numbers that divide exactly into another number. For example, the factors of 8 are 1, 2, 4, and 8. Common factors are shared by two or more numbers, like 2, 5, and 10 for 30 and 20. The highest common factor (HCF) is the largest factor common to two or more numbers. It can be found by listing factors or using prime factorization. For example, the HCF of 30 and 36 is 6, found by listing or prime factorization: $30 = 2 \times 3 \times 5$ and $36 = 2 \times 2 \times 3 \times 3$.

Exam Tips

• Understand the Basics: Make sure you know the definitions of multiples, factors, common multiples, and common factors.
• Practice LCM and HCF: Use both listing and prime factorization methods to find the LCM and HCF. This will help you choose the best method during exams.
• Use Factor Trees: Drawing factor trees can simplify finding the prime factors of a number, which is crucial for calculating the HCF.
• Memorize Key Multiples: Knowing the times tables well can speed up finding multiples and common multiples.
• Check Your Work: Always verify your answers by multiplying back to ensure accuracy, especially in factorization problems.