🔵Factors, Multiples, Prime & Composite
A factor divides a number exactly; a multiple is the times-table of a number. A prime number has exactly two factors (1 and itself); a composite number has more than two.
Example: factors of 12 = 1, 2, 3, 4, 6, 12. Multiples of 4 = 4, 8, 12, 16, …
👀 See a worked example
List the factors of 18.
1, 2, 3, 6, 9, 18.
Is 13 prime or composite?
Only factors 1 and 13 → prime.
🤖 Vidi's Key Points
- A factor divides exactly; a multiple is the times-table.
- Prime = 2 factors; composite = more than 2.
- 1 is neither prime nor composite.
🟢HCF & LCM
The HCF (Highest Common Factor) is the biggest number that divides two numbers exactly. The LCM (Lowest Common Multiple) is the smallest number that is a multiple of both.
Example — 12 and 18: common factors are 1, 2, 3, 6 → HCF = 6. Multiples of 4 and 6 first meet at 12 → LCM(4,6) = 12.
👀 See a worked example
Find the HCF of 8 and 12.
Common factors: 1, 2, 4 → HCF = 4.
Find the LCM of 3 and 5.
First common multiple is 15.
🤖 Vidi's Key Points
- HCF = biggest number dividing both (use common factors).
- LCM = smallest number that is a multiple of both.
- For two numbers with no common factor, the LCM is their product.
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