Summary and Exam Tips for Factors and Multiples
Factors and Multiples is a subtopic of Number, which falls under the subject Mathematics in the Cambridge Lower Secondary curriculum. Multiples of a number are the numbers that can be divided by that number without leaving a remainder. They are essentially the numbers found in that number's times table. For instance, the multiples of 3 are 3, 6, 9, 12, etc. Common multiples are numbers that are multiples of two or more numbers, such as 40 being a common multiple of 4 and 5. The Lowest Common Multiple (LCM) is the smallest multiple shared by two or more numbers. For example, 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 numbers that are factors of two or more numbers, like 2, 5, and 10 being common factors of 30 and 20. The Highest Common Factor (HCF) is the largest factor shared by two or more numbers. It can be found by listing factors or using prime factorization. For instance, the HCF of 30 and 36 is 6, found by identifying common prime factors.
Exam Tips
- Understand Definitions: Ensure you know the definitions of key terms like multiples, factors, LCM, and HCF.
- Practice Listing: Practice listing factors and multiples to quickly identify common ones.
- Use Prime Factorization: For larger numbers, use prime factorization to find the HCF efficiently.
- Memorize Times Tables: Being familiar with times tables can help you quickly identify multiples.
- Solve Examples: Work through example problems to reinforce your understanding and speed up problem-solving during exams.
