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Finding Factors Systematically

Part of Factors, Multiples & Primes — GCSE Mathematics

This study notes covers Finding Factors Systematically within Factors, Multiples & Primes for GCSE Mathematics. Revise Factors, Multiples & Primes in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 3 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 8

Practice

14 questions

Recall

22 flashcards

Finding Factors Systematically

Example: Find all factors of 36

Method 1: Factor Pairs

  • 1 × 36 = 36 → factors: 1, 36
  • 2 × 18 = 36 → factors: 2, 18
  • 3 × 12 = 36 → factors: 3, 12
  • 4 × 9 = 36 → factors: 4, 9
  • 6 × 6 = 36 → factor: 6
  • Stop when factors start repeating

Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36

Keep building this topic

Read this section alongside the surrounding pages in Factors, Multiples & Primes. That gives you the full topic sequence instead of a single isolated revision point.

Key DefinitionsPrime Factor TreesBuilding Blocks of NumbersFinding HCF and LCM

Practice Questions for Factors, Multiples & Primes

Which of these numbers is prime?

  • A. 27
  • B. 29
  • C. 33
  • D. 35
1 markfoundation

Explain why 51 is not a prime number.

2 marksstandard

Quick Recall Flashcards

Factor
A number that divides exactly into another number with no remainder. Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Multiple
A number in the times table of another number. Example: Multiples of 5 are 5, 10, 15, 20, 25, 30...

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Key Definitions

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Prime Factor Trees