All About Maths

Factors and multiples (8300 - Higher - Number)

Topic:Factors and multiples

Route Map

Specification references (in recommended teaching order)

Specification content Specification notes
N4
  • Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation, and the unique factorisation theorem
  • prime factor decomposition including product of prime factors written in index form
N5
  • Apply systematic listing strategies and the use of the product rule for counting
  • including using lists, tables and diagrams


The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

Teaching resources

Factors and multiples - all resources for 3 year route map - zip folder
Downloadable resource in zip format. 07/09/2015
4.1 MB
Related resources: Factors and multiples
Topic overview and lesson plans
Downloadable resource in doc format. 07/09/2015
189 KB
Related resources: Factors and multiples

Lesson 2 Activity 1
Downloadable resource in ppt format. 07/09/2015
1.3 MB
Related resources: Factors and multiples
Lesson 3 Activity 1
Downloadable resource in doc format. 07/09/2015
208 KB
Related resources: Factors and multiples
Lesson 3 Activity 2
Downloadable resource in doc format. 07/09/2015
201 KB
Related resources: Factors and multiples
Lesson 4 Activity 1
Downloadable resource in ppt format. 07/09/2015
1.4 MB
Related resources: Factors and multiples

Lesson 1 Worksheet 1
Downloadable resource in doc format. 07/09/2015
201 KB
Related resources: Factors and multiples
Lesson 1 Worksheet 2
Downloadable resource in doc format. 07/09/2015
202 KB
Related resources: Factors and multiples
Lesson 3 Worksheet 1
Downloadable resource in doc format. 07/09/2015
478 KB
Related resources: Factors and multiples
Lesson 3 Worksheet 2
Downloadable resource in doc format. 07/09/2015
248 KB
Related resources: Factors and multiples
Lesson 3 Worksheet 3
Downloadable resource in doc format. 07/09/2015
202 KB
Related resources: Factors and multiples

Lesson 1 Homework sheet 1
Downloadable resource in doc format. 07/09/2015
349 KB
Related resources: Factors and multiples
Lesson 1 Homework sheet 2
Downloadable resource in doc format. 07/09/2015
220 KB
Related resources: Factors and multiples
Lesson 2 Homework sheet 1
Downloadable resource in doc format. 07/09/2015
202 KB
Related resources: Factors and multiples
Lesson 2 Homework sheet 2
Downloadable resource in doc format. 07/09/2015
228 KB
Related resources: Factors and multiples
Lesson 3 Homework sheet 1
Downloadable resource in doc format. 07/09/2015
205 KB
Related resources: Factors and multiples
Lesson 4 Homework sheet 1
Downloadable resource in doc format. 07/09/2015
203 KB
Related resources: Factors and multiples

Diagnostic Questions - Factors and Multiples
AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic question assessment for our new 2017 GCSE Maths specification.24/02/2016
E-library
Type(s): Diagnostic Questions (e-library)

Co-primes: Teacher Notes
Teacher notes which guide an investigation into co-prime numbers.19/05/2015
E-library
Type(s): Overview (e-library)

Can you find a perfect number?
An introduction to the idea of a 'perfect' number, from which students must investigate to find other perfect numbers and consider other properties involving factors.19/05/2015
E-library
Type(s): Activities (e-library)
HCF and LCM
Activities involving HCF and LCM with demanding 2 or 3 digit numbers.19/05/2015
E-library
Type(s): Activities (e-library)
HCF, LCM, Product of Prime Factors tarsia
A tarsia card sorting activity which forms a hexagon. Questions involve prime factor decomposition, HCF and LCM. You will need to register for a TES account to access this resource, this is free of charge.19/05/2015
E-library
Type(s): Activities (e-library)
Prime Factorization
Prime numbers interactive worksheet. An introduction to prime factorization, followed by six questions assessing understanding.29/08/2014
E-library
Type(s): Activities (e-library) | Worksheets (e-library)

Weekly Problem 16 - 2006
A student investigation which requires consideration of multiples.19/05/2015
E-library
Type(s): Plenaries (e-library)

Prime Factorization
Prime numbers interactive worksheet. An introduction to prime factorization, followed by six questions assessing understanding.29/08/2014
E-library
Type(s): Activities (e-library) | Worksheets (e-library)

Venn Multiples
An interactive website in which students must place numbers in the correct area of the Venn diagram, depending on what they are multiples of. The activity can be varied by changing the required multiples.19/05/2015
E-library
Type(s): Game (e-library)

Eratosthenes' Sieve
Online demonstration which uses the principles of Eratosthenes' Sieve to identify the prime numbers between 1 and 100.19/05/2015
E-library
Type(s): Miscellaneous (e-library)

Collecting Data - Organising Data - Repeating Numbers - Problem Sheet
Downloadable resource in doc format. 01/02/2010
168 KB
Related resources: Higher | Unit 1 | Collecting Data | Basic number, factors and multiples | Basic number | Factors and multiples | Problem Sheets
Ratio and Proportion - Golf - Golf Scores - Problem Sheet and Answers
Downloadable resource in doc format. 07/05/2010
215 KB150 KB
Related resources: Higher | Unit 1 | Ratio and Proportion | Basic number, factors and multiples | Basic number | Factors and multiples | Problem Sheets
Ratio and Proportion - Golf - Holes and Distances - Supplementary Resource
Downloadable resource in xls format. 08/05/2010
43 KB
Related resources: Higher | Unit 1 | Ratio and Proportion | Basic number, factors and multiples | Basic number | Factors and multiples | Supplementary Resources
Ratio and Proportion - Golf - Par Cards - Supplementary Resource
Downloadable resource in xls format. 09/05/2010
40 KB
Related resources: Higher | Unit 1 | Ratio and Proportion | Basic number, factors and multiples | Basic number | Factors and multiples | Supplementary Resources
Ratio and Proportion - Maths and Golf - Lesson Plan
Downloadable resource in doc format. 10/05/2010
169 KB
Related resources: Higher | Unit 1 | Ratio and Proportion | Basic number, factors and multiples | Basic number | Factors and multiples | Lesson Plans

Topic Tests

8300 GCSE Higher Product of Primes (HCF and LCM) Mark Scheme
Downloadable resource in pdf format. 09/09/2022
237 KB
Related resources: Basic number, factors and multiples | Factors and multiples
8300 GCSE Higher Product of Primes (HCF and LCM) Topic Test
Downloadable resource in pdf format. 09/09/2022
209 KB
Related resources: Basic number, factors and multiples | Factors and multiples
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