Prior Content: Sequences, Basic Operations +-x/, Indices
Possible Next Steps: Surds, Sets, Combinations, Algebraic Proof
Contents
- 1.1 Key Groups of Numbers
- 2.1 Prime Factors
- 3.1.1 Highest Common Factors & Lowest Common Multiples by Listing
- 3.1.2 Highest Common Factors & Lowest Common Multiples by Prime Factors
- 3.2 HCFs & LCMs in Context
- 3.3 HCFs & LCMs of Algebraic Terms
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Key Groups of Numbers
To look at Number Groups/ Sets please go to the Sets Course Support Page
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Even Numbers & Odd Numbers
Corbett Maths Factors
Corbett Maths Multiples
Corbett Maths Prime Numbers
Corbett Maths Triangular Numbers
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Miss Konstantine (MathsHKO)
- Math = Love (Sarah Carter)
- Multiples Maths Maze collection
- Factors & Multiples activities
- Multiples of 7 Maths Maze
- Multiples of 6 Maths Maze
- Prime & Composite activities
- Composite Numbers Maths Maze
- Perfect Squares Mystery Picture
- Prime Numbers chart 1-1000
- Prime Numbers Mystery Picture
- Factor Pairs chart 1-100
- Real Number System activities
- Real Number System card activity
- Factors Race activity
- Sieve of Eratosthenes Activity
- Primes Below 100 Chart
- Real Number System Dice Activity
- Prime Numbers Poster
- Prime & Composite Chart
- Rational & Irrational Exploration
- Real Number Nesting Boxes
- Real Number Line Project
- Subsets of Real Numbers Organiser
- Real Number System Organiser
- Prime Factorisation
- Don Steward
- The Chalkface
- Very Strange Game: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
- Prime Sieve: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
- 100 Lockers: PowerPoint
- Fact cards✦
- Transum
- Interactive Maths
- 100 Square & Number Properties: Multiples | Types of Numbers | Number Properties
- Goal Free Problems
- Go Teach Maths
- thewessens.net Classroom Apps
- Factor Explorer (drag squares into rectangles to find all the factors of a number)
- Multiple Madness (timed game sorting numbers as multiples, squares or primes)
- MathsPad
- IsThisPrime
- MathsBot
- MathCelebrity
- deselby
- Mr Chapman Maths
- happymathematician
- Mr Thompson Maths
- Grid Number (Dave Hewitt & Jonathan Hall)
- Finding Primes (interactive) (shade the primes on a 6-column grid)
- NCETM
- NCETM Key Idea: Identifying multiples of an integer (PowerPoint)
- WW Grid Activities
Worksheets
- Dr Austin Maths
- Factors, Multiples and Primes Practice Grid (Word | PDF | Answers)
- Factors, Multiples and Primes Decode the Joke (Word | PDF | Answers)
- Factors Practice Strips (Word | PDF | Answers)
- Factor Bugs Activity (Word | PDF✦ | Answers✦)
- Factors True or False (Word | PDF✦ | Answers✦)
- Multiples Practice Strips (Word | PDF | Answers)
- Multiples True or False (Word | PDF✦ | Answers✦)
- Factors, Multiples and Primes Decode the Joke (Word | PDF✦ | Answers✦)
- Factors and Multiples Crack the Code (Word | PDF | Answers)
- Investigating Prime Activity (Word | PDF | Answers)
- Prime Crack the Code (Word | PDF✦ | Answers✦)
- Corbettmaths
- Multiples, Factors & Primes Practice Questions & Solutions
- Factors Worksheet & Solutions
- Multiples Worksheet & Solutions
- Prime Numbers Worksheet & Solutions
- Triangular Numbers Practice Questions, Solutions & Video Solutions
- Triangular Numbers Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
- CIMT MEP (online self-checking)
- Maths Genie
- Factors and Multiples: Booklet · Worksheet · Solutions · Lesson · Topic page
- MME
- @taylorda01
- Mr Morley Maths
- Primes, Squares and Cubes: Notes jotter/worksheet · Exam questions · Rehearsal strip · Answers
- Pret Homework (@frimymaths)
- Multiples (@frimymaths, docx)
- Pret Homework (Tom Kendall)
- Number Properties (Tom Kendall, docx)
Dr Frost Resources
Dr Frost Video
K21: Identify Odd and Even Numbers.
K22: Identify Square Numbers.
K23: Identify Cube Numbers.
K59: Find Factors of a Number.
K60: Find Multiples of a Number.
K61: Identify Prime Numbers.
Dr Frost Slides & Activities
Dr Frost Slides (1-4 & 10)
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 5a: Identify odd and even numbers.
- 52b: Identify multiples of a number greater than 12.
- 52c: Write the first 3 multiples of a number.
- 52d: Write all the multiples of a number in a range.
- 53a: Identify a factor of a number.
- 53b: Find factor pairs of a number.
- 53c: List all factors of a number.
- 88b: Identify square numbers.
- 88c: Identify cube numbers.
- 94a: Identify common multiples of 2 numbers by listing.
- 94b: Identify common multiples of more than 2 numbers by listing.
- 95a: Identify common factors of 2 numbers by listing.
- 95b: Identify common factors of more than 2 numbers by listing.
- 97b: Determine whether a number is prime, up to 100.
- 97c: List prime numbers in a range or prime numbers in sequence after a stated prime.
- 97d: Determine whether a given number is prime, even/odd, square and cube.
- 97e: Use the sieve of Eratosthenes to determine the list of all primes up to a given number.
- 333a: Determine whether a number is in mathbbN and/or mathbbZ
- 333b: Determine if a number is rational or irrational.
- 333c: Determine whether a number is in mathbbN, mathbbZ, mathbbR and/or mathbbQ
- 5: Exam Practice: Odd and even numbers
- 52: Exam Practice: Multiples of a number
- 53: Exam Practice: Factors of a number
- 88: Exam Practice: Power notation and calculate simple powers, e.g. squares, cubes
- 94: Exam Practice: Common multiples by listing
- 95: Exam Practice: Common factors by listing
- 97: Exam Practice: Prime numbers
- 333: Exam Practice: Infinite number sets
Extension Materials
Other Videos & Multimedia
Enrichment Video
Numberphile: 1 is NOT Prime
2.1 Prime Factors
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Product of Primes
Online Platforms (with Videos & Exercises)
- Khan Academy
- Prime factorisation: Videos & practice
Activities & Resources
- Craig Barton Variation Theory Webpage & Product of Prime Factors ppt
- Maths 4 Everyone
- Mr Mawson Prime Factor Decomposition Logical Puzzle✦ (TES Account Required)
- thewessens.net Prime Factorisation versus game
- Andy Lutwyche
- Miss Konstantine (MathsHKO)
- Math = Love (Sarah Carter)
- Don Steward
- The Chalkface
- Prime Factor Grids: PDF
- Prime Factor decomposition activity✦
- Transum
- Interactive Maths
- Product of Primes: QQI | 10QQI | Count Down | Relay | Bingo
- Product of Primes: Worksheets
- Mr Draper Maths Product of Primes: Extending and Deepening Understanding
- Go Teach Maths
- thewessens.net Classroom Apps
- About Primes (prime factorisation, its uniqueness and the Sieve of Eratosthenes)
- variationtheory.com
- MathsPad
- MathsBot
- Mr Thompson Maths
- BossMaths
- Duncan Grantham
- Ticktock Maths
- The product of primes lesson (slides)
Worksheets
- Dr Austin Maths
- Trees Practice Strips (Word | PDF | Answers)
- Decomposition with Factor Trees Fill in the Blanks (Editable Word | PDF | Answers)
- More Prime Factor Decomposition with Factor Trees Fill in the Blanks (Word | PDF | Answers)
- Decomposition Practice Strips (Word | PDF | Answers)
- Puzzle (Word | PDF✦ | Answers✦)
- Investigating Prime Factors Activity (Word | PDF | Answers)
- Investigating Prime Factors of Squares and Cubes (Word | PDF | Answers)
- Trees Practice Strips (Word | PDF | Answers)
- Decomposition with Factor Trees Fill in the Blanks (Word | PDF | Answers)
- More Prime Factor Decomposition with Factor Trees Fill in the Blanks (Word | PDF | Answers)
- Corbettmaths
- Product of Primes, HCF’s & LCM’s Practice Questions (Q1-9) & Solutions
- Product of Primes Worksheet & Solutions
- CIMT MEP (online self-checking)
- Maths Genie
- Prime Factors, HCF and LCM: Booklet · Worksheet · Solutions · Lesson · Topic page
- Kuta Software
- Access Maths
- 1st Class Maths
- @taylorda01
- Starting Points Maths
- Primes, HCF, LCM (by Kieran McConville) · PDF
- Mr Morley Maths
- Prime Factors: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme · Rehearsal strip · Answers
Dr Frost resources
Dr Frost Video
K215: Write a Number as the Product of its Prime Factors.
Dr Frost Slides & Activities
Dr Frost Slides (5)
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 161a: Write a number below 100 as the product of its prime factors.
- 161b: Write a number over 100 as the product of its prime factors.
- 161c: Write a product as the product of its prime factors.
- 161d: Write a product as the product of its prime factors, where some powers are algebraic.
- 164a: Identify specific factors of a number expressed as a product of powers.
- 164b: Know the properties of the prime factorisation of a square or cube number.
- 164c: Work out the number of digits of a number or the number of trailing zeroes where the number is expressed as a product of factors.
- 164d: Identify the number of factors of a number by using its prime factorisation.
- 161: Exam Practice: Prime factorisation of a number
- 164: Exam Practice: Properties of a number based on its prime factorisation (e.g. identify factors, if it is square, trailing zeroes)
EXTENSION MATERIALS
Other Videos & Multimedia
Using Product of Primes to Find Square or Cube Numbers
3.1.1 Highest Common Factors & Lowest Common Multiples by Listing
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths LCM & Common Multiples
Corbett Maths Common Factors & HCF
Online Platforms (with Videos & Exercises)
- Khan Academy
- Highest common factor: Videos & practice
- Lowest common multiple: Videos & practice
Activities & Resources
- Maths 4 Everyone
- Math = Love (Sarah Carter)
- Don Steward
- Transum
- Access Maths
- Factors & Multiples Games: Last One Standing Game | Game Cards
- HCF & LCM: HCF (Fluency & Reasoning) | LCM (Fluency & Reasoning)
- Interactive Maths
- HCF & LCM: QQI | 10QQI | Count Down | Relay | Bingo
- HCF & LCM: Worksheets
- Go Teach Maths
- Ticktock Maths
- Highest Common Factor lesson (slides)
- Lowest Common Multiple lesson (slides)
- Grid Number (Dave Hewitt & Jonathan Hall)
- Common Multiples (interactive) · PDF · Word
Worksheets
- Dr Austin Maths
- Practice Strips (Word | PDF | Answers)
- Fill In The Blanks (Word | PDF | Answers)
- Practice Strips (Word | PDF | Answers)
- Fill In The Blanks (Word | PDF | Answers)
- LCM and HCF Practice Strips (Word | PDF | Answers)
- Practice Strips (Word | PDF | Answers)
- Match-Up (Word | PDF | Answers)
- Fill In The Blanks (Word | PDF | Answers)
- Match-Up (Word | PDF | Answers)
- Fill In The Blanks (Word | PDF | Answers)
- Corbettmaths
- Maths 4 Everyone
- Miss Konstantine (MathsHKO)
- Kuta Software
- MME
- Mr Morley Maths
- Factors and Multiples: Notes jotter/worksheet · How-to sheet · Exam questions
- Pret Homework (Phil Aldridge)
- HCF and LCM (Phil Aldridge, docx)
Dr Frost resources
Dr Frost Video
K216: Find the HCF of Two Numbers Using a Listing Strategy.
K219: Find the LCM of Two Numbers Using a Listing Strategy.
Dr Frost Slides & Activities
Dr Frost Slides (7-12)
Topic Tests
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 96a: Determine the LCM of two numbers using a listing strategy.
- 96b: Determine the LCM of more than two numbers using a listing strategy.
- 96c: Determine the HCF of two numbers using a listing strategy.
- 96d: Determine the HCF of more than two numbers using a listing strategy.
- 96: Exam Practice: Highest Common Factor and Lowest Common Multiple by listing
EXTENSION MATERIALS
3.1.2 Highest Common Factors & Lowest Common Multiples by Prime Factors
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths LCM HCF Using Product of Primes
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Don Steward
- The Chalkface
- Prime Venn diagram: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
- Interactive Maths
- HCF & LCM using Prime Factors: Video
- Go Teach Maths
- NCETM
- NCETM Key Idea: Using prime factorisation for HCF (PowerPoint)

Unknown Author
Worksheets
- Dr Austin Maths
- LCM and HCF Using Repeated Division Fill In The Blanks (Word | PDF | Answers)
- LCM and HCF Using Venns Fill In The Blanks (Word | PDF | Answers)
- Using Venns for HCF and LCM Problems Practice Strips (Word | PDF | Answers)
- LCM and HCF Crack the Code (Word | PDF | Answers)
- LCM and HCF from Prime Factorisation Practice Strips (Word | PDF | Answers)
- LCM and HCF Using Repeated Division Fill In The Blanks (Word | PDF | Answers)
- LCM and HCF Using Venns Fill In The Blanks (Word | PDF | Answers)
- LCM and HCF Crack the Code (Word | PDF | Answers)
- Corbettmaths
- Product of Primes, HCF’s & LCM’s Practice Questions (Q10 Onwards) & Solutions
- Product of Primes: HCF & LCM Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
- CIMT MEP (online self-checking)
- Mathshelper (Jon Stone)
- Access Maths
- MME
- Starting Points Maths
- Pret Homework (@MissBsResources)
- HCF & LCM Venn Diagrams (@MissBsResources, pdf)
Dr Frost resources
Dr Frost Video
K217: Find the HCF of Two Numbers Which are Already Prime Factorised.
K218: Find the Highest Common Factor (HCF) of 2 numbers by Prime Factorising.
K220: Find the LCM of Two Numbers Which are Already Prime Factorised.
K221: Find the Lowest Common Multiple (LCM) of 2 Numbers by Prime Factorising.
Dr Frost Slides & Activities
Dr Frost Slides (7-12)
Topic Tests
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 162a: Determine the HCF of two numbers which are already prime factorised.
- 162b: Determine the LCM of two numbers which are already prime factorised.
- 162c: Determine the Highest Common Factor (HCF) of 2 numbers by prime factorising.
- 162d: Determine the Lowest Common Multiple (LCM) of 2 numbers by prime factorising.
- 162e: Determine the Highest Common Factor (HCF) of more than 2 numbers by prime factorising.
- 162f: Determine the Lowest Common Multiple (LCM) of more than 2 numbers by prime factorising.
- 162g: Write a fraction in simplest form by prime factorisation to find the HCF.
- 162: Exam Practice: Lowest Common Multiple or Highest Common Factor by prime factorisation
EXTENSION MATERIALS
3.2 HCFs & LCMs in Context
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
When to use LCM & HCF? Keywords to help spot LCM and HCF problems by Maxtute CBSE Math – Classes 9 to 12
LCM and GCF word problems by Khan Academy
LCM and GCF word problems by Jean Wanamaker
Online Platforms (with Videos & Exercises)
Activities & Resources
- Andy Lutwyche
- Don Steward
- thewessens.net Classroom Apps
- The Rate Escape (game: work out when rotating rings line up, a lowest common multiple problem)
- Addvance Maths
- CP3 Maths (cparkinson3)
- MathBits
Worksheets
- Dr Austin Maths
- Corbettmaths
- LCM’s & HCF’s Practice Questions & Solutions
- Pixi Maths
- Naiker Maths
- HCF & LCM: Worksheet
- 1st Class Maths
Dr Frost resources
Dr Frost Slides & Activities
Dr Frost Slides (13)
Topic Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 94c: Solve problems in context using common multiples by listing.
- 95c: Solve problems in context using common factors by listing.
- 96e: Use the Lowest Common Multiple in an applied setting.
- 96f: Use the Highest Common Factor in an applied setting.
- 162j: Solve problems involving LCM and HCF where one or more of the numbers is unknown.
- 94: Exam Practice: Common multiples by listing
- 95: Exam Practice: Common factors by listing
- 96: Exam Practice: Highest Common Factor and Lowest Common Multiple by listing
- 162: Exam Practice: Lowest Common Multiple or Highest Common Factor by prime factorisation
Further Practice
- Practise Questions
EXTENSION MATERIALS
3.3 HCFs & LCMs of Algebraic Terms
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Finding the greatest common factor of two monomials by Khan Academy
Online Platforms (with Videos & Exercises)
Activities & Resources
- Transum
Worksheets
- Kuta Software
Dr Frost resources
Dr Frost Slides & Activities
Dr Frost Slides (13)
Topic Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 162h: Determine the HCF of two or more algebraic expressions.
- 162i: Determine the LCM of two or more algebraic expressions.
- 162: Exam Practice: Lowest Common Multiple or Highest Common Factor by prime factorisation
Further Practice
- Practise Questions
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Properties of Numbers PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Factors and multiples as PowerPoint or PDF
Worksheets
- Dr Austin Maths
- Maths 4 Everyone
- MathedUp
- HCF, LCM & Prime Factorisation: Worksheet · Practice · Quiz · Question Gallery
- Mathsaurus (Kevin Olding)
- Physics & Maths Tutor
Activities
- NRICH (student problems)
- Don Steward
- Dr Austin Maths
- MathsPad
- Stephen Bodman
Online Platforms
- Khan Academy
- Prime numbers: Videos & practice
Online Platforms
- Khan Academy
- Greatest common factor of monomials: Videos & practice
External
- NCETM
- NCETM Checkpoints: Properties of number (factors, multiples, squares, cubes) (diagnostic tasks)
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.