Factors & Multiples
Calculators, worked examples and guides — from finding factors and multiples through to HCF, LCM and prime factorisation.
Learning about Factors & Multiples
The key idea: factors divide into a number exactly; multiples come out of a number. Understanding both unlocks fraction simplification, common denominators, and much of number theory. They are tools, not just topics.
Type 1 — Finding factors
"List all factors of 24"
Work in pairs systematically: 1×24, 2×12, 3×8, 4×6.
Stop when the pairs meet.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Shortcut: Always work in factor pairs — you cannot miss any this way
Type 2 — Highest Common Factor (HCF)
"Find the HCF of 18 and 24"
Step 1: Factors of 18: 1, 2, 3, 6, 9, 18.
Step 2: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Step 3: Common factors: 1, 2, 3, 6 → HCF = 6
Shortcut: Use prime factorisation for large numbers — HCF uses the lowest power of each shared prime
Type 3 — Lowest Common Multiple (LCM)
"Find the LCM of 4 and 6"
Step 1: Multiples of 4: 4, 8, 12, 16, 20...
Step 2: Multiples of 6: 6, 12, 18...
Step 3: First match: 12 → LCM = 12
Shortcut: For LCM using prime factorisation — use the highest power of each prime factor
Factors & Number Rules Formula Sheet
Need a printable revision sheet? Access rules for highest common factor (HCF), lowest common multiple (LCM), prime factorisation, and index laws with step-by-step worked examples and custom print export.
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Factors Questions Answered
What is a factor?
A factor is a whole number that divides exactly into another number with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.
What is a multiple?
A multiple is the result of multiplying a number by a positive whole number. The multiples of 5 are 5, 10, 15, 20, 25 and so on.
What is the highest common factor (HCF)?
The HCF is the largest number that divides exactly into two or more numbers. The HCF of 12 and 18 is 6, because 6 is the largest number that goes into both.
What is the lowest common multiple (LCM)?
The LCM is the smallest number that is a multiple of two or more numbers. The LCM of 4 and 6 is 12, because 12 is the smallest number in both the 4 and 6 times tables.
What is prime factorisation?
Writing a number as a product of its prime factors. For example: 60 = 2² × 3 × 5. Every integer greater than 1 has a unique prime factorisation — a fact known as the Fundamental Theorem of Arithmetic.