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This topic covers prime numbers and simple number proofs, expressing numbers as products of primes and reasoning about factors, multiples and divisibility to justify statements. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Express the numbers algebraically using their prime factorisation, then argue from the structure. To show a number cannot be prime, find a factor. To show two numbers are coprime, show their prime factorisations share nothing.
Before you start
Assumed knowledge: prime factorisation and algebraic notation. Expect to use it again in higher-tier proof questions.
What you learn
Primes are the atoms of number, and proof is how we show a statement is always true. A number’s prime factorisation reveals its structure. To prove something is always true, you can’t just test examples — you use algebra to cover every case at once. A proof must work for every case — so use algebra, not examples. The course works through prime factorisation and properties, algebra for odd, even and consecutive and building proofs and counterexamples. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Primes & Proof as one of the Number topics in our GCSE course library, at Higher tier. There are 3 teaching sections and 2 fully worked examples, plus 3 sets of check questions. Nearby topics in the same strand are Product Rule for Counting, Reverse Percentages, Rounding & Estimation and Significant Figures & Truncation. Endless extra practice on this strand is available on the Number revision engine, which generates a fresh question each time.
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