Summary
Factors and multiples are fundamental concepts in mathematics that help in understanding number relationships.
- Multiples — numbers that a given number will divide into. Example: The multiples of 3 are 3, 6, 9, 12, 15.
- Common Multiples — a number that is a multiple of two or more numbers. Example: 40 is a common multiple of 4 and 5.
- Lowest Common Multiple (LCM) — the smallest number that two or more numbers share as a multiple. Example: The LCM of 4 and 5 is 20.
- Factors — numbers that divide exactly into another number. Example: The factors of 8 are 1, 2, 4, 8.
- Common Factors — numbers that are factors of two or more numbers. Example: 2, 5, and 10 are common factors of 30 and 20.
- Highest Common Factor (HCF) — the greatest factor that divides into two or more numbers. Example: The HCF of 30 and 36 is 6.
Exam Tips
Key Definitions to Remember
- Multiples are numbers that a given number will divide into.
- Common multiples are shared multiples of two or more numbers.
- The LCM is the smallest common multiple of two or more numbers.
- Factors are numbers that divide exactly into another number.
- Common factors are shared factors of two or more numbers.
- The HCF is the greatest common factor of two or more numbers.
Common Confusions
- Confusing multiples with factors.
- Mixing up LCM and HCF.
Typical Exam Questions
- What are the first three multiples of 5? 5, 10, 15
- Find the LCM of 3 and 4. 12
- List the factors of 12. 1, 2, 3, 4, 6, 12
What Examiners Usually Test
- Ability to identify and list multiples and factors.
- Understanding of how to find common multiples and factors.
- Calculation of LCM and HCF using different methods.