Summary
Factors and multiples are fundamental concepts in mathematics that help in understanding division and multiplication relationships between numbers.
- Multiple — a number that can be divided by another number without leaving a remainder. Example: 12 is a multiple of 3 and 4.
- Factor — a number that can evenly divide another number. Example: 3 is a factor of 12.
- Prime Factor — a factor that is a prime number, used to express a number as a product of prime numbers. Example: The prime factors of 36 are 2 and 3.
- Highest Common Factor (HCF) — the greatest number that can divide two or more numbers. Example: The HCF of 12 and 16 is 4.
- Lowest Common Multiple (LCM) — the smallest number that is a multiple of two or more numbers. Example: The LCM of 6 and 10 is 30.
Exam Tips
Key Definitions to Remember
- A multiple is a number that can be divided by another number without a remainder.
- A factor is a number that divides another number evenly.
- Prime factors are prime numbers that multiply to give the original number.
- The HCF is the largest factor common to two or more numbers.
- The LCM is the smallest multiple common to two or more numbers.
Common Confusions
- Confusing factors with multiples.
- Forgetting that prime factors must be prime numbers.
Typical Exam Questions
- What is the HCF of 60 and 114? Answer: 6
- Write 98 as a product of its prime factors. Answer: 2 x 7 x 7
- Find the LCM of 120 and 150. Answer: 600
What Examiners Usually Test
- Ability to find the HCF and LCM of given numbers.
- Writing numbers as a product of their prime factors.
- Understanding and identifying factors and multiples in various contexts.