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Multiples, Factors and Prime Factorisation

CAPS Senior Phase Mathematics (South Africa): Grade 8–9

8 ready-made resources for teaching Multiples, Factors and Prime Factorisation, written for CAPS Senior Phase Mathematics. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where learners usually go wrong, free to read whether or not you sign up.

Independently rechecked. These files were written to the specification from our own topic maps, then put through a separate recheck pass from the one that wrote them, which found and fixed real errors. A subject teacher has not signed them off individually, so give them your usual read before you teach from them.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Worksheet (Grade 8 & 9)Word, editable
Worksheet mark schemeWord, editable

Grade 8

Find the factors and multiples of a number, and determine the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two or more numbers: all carried forward from Grade 7, which already covers multiples and LCM (e.g. finding the LCM of 6 and 18) alongside factors, HCF, and prime factors of three-digit numbers.
Find the HCF and LCM of two- and three-digit numbers specifically, using inspection or the ladder method, or by prime factorisation: the extended number range and the ladder-method technique are what's genuinely new at Grade 8, not the underlying HCF/LCM concept itself.
Use prime factorisation as a method to determine the square root of a number: this is a specific technique new at Grade 8: break a number into its prime factors, then pair matching primes to find the root, rather than only listing prime factors as Grade 7 did.

Grade 9, in addition

No new content is listed in the CAPS table beyond Grade 8. Grade 9 content elsewhere (for example, simplifying surds in the Theorem of Pythagoras topic, or finding a common factor when factorising algebraic expressions) draws on these Grade 8 skills as a prerequisite rather than extending them further as their own topic.

Where learners go wrong

Confusing a factor of a number with a multiple of it (e.g. treating 3 as "a multiple of 12" instead of "a factor of 12").
Finding a common factor or common multiple of two numbers, but not the highest common factor or lowest common multiple specifically asked for.
When using prime factorisation to find a square root, forgetting to pair matching prime factors correctly, or stopping the factor tree before reaching only prime numbers.
Treating 1 as a prime number, or missing it as a factor of every number.

How it gets asked in the exam

"Determine the factors of ...", "Determine the HCF of ... and ...", "Determine the LCM of ... and ...", "Use prime factorisation to determine the square root of ...", "Write ... as a product of its prime factors".

Key vocabulary

Factor, multiple, Highest Common Factor (HCF), Lowest Common Multiple (LCM), prime number, prime factor, prime factorisation.

Assumed prior knowledge

Multiplication and division facts.
Factors and prime factors of three-digit numbers (Grade 7 content, at a level this topic builds directly on).

How Speca scaffolds this topic

Use a consistent factor-tree visual for prime factorisation, with matching prime pairs highlighted in the same colour when the technique is applied to finding a square root. For HCF/LCM specifically, also teach the ladder method (repeated division by a common prime, written as a vertical "ladder") alongside the tree: this is the method named directly in CAPS and likely to match what South African teachers already use in class.
Provide a short, fixed reference list of the first several prime numbers (2, 3, 5, 7, 11, 13...) so learners aren't re-deriving primality every time, mirroring the equivalent scaffold already used for surd simplification in the Pythagoras topic.
Keep factor and multiple work visually distinct (e.g. factors always shown "branching down from" a number, multiples always shown "counting up from" a number) to reduce the two concepts being confused.

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