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Door 4 · Grade 5

🔢 Factors, Multiples, HCF & LCM

A factor divides exactly; a multiple is the times-table

▶ Play Door 4

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, …

Worked example

Problem: List the factors of 18.

  1. 1, 2, 3, 6, 9, 18.

Answer: 1, 2, 3, 6, 9, 18.

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.

Worked example

Problem: Find the HCF of 8 and 12.

  1. Common factors: 1, 2, 4 → HCF = 4.

Answer: Common factors: 1, 2, 4 → HCF = 4.