Prime & Composite Numbers
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- What Is a Prime Number?
Identify numbers with exactly two factors - Finding Primes
Test whether numbers are prime - Prime Factorisation
Express numbers as products of prime factors - Challenge — Primes in Problem Solving
Use prime factors to solve problems
Common Mistakes
- Thinking 1 is a prime number
1 is NOT a prime number. A prime must have exactly two factors: 1 and itself. The number 1 only has one factor (itself), so it does not qualify. The smallest prime is 2. - Thinking all odd numbers are prime (e.g. believing 9 or 15 are prime because they are odd)
Being odd does not make a number prime. 9 = 3 × 3 and 15 = 3 × 5, so neither is prime. Check by trying to divide by 2, 3, 5, and 7 — if any divides evenly, the number is not prime. - Thinking 2 is not prime because it is even
2 is the ONLY even prime number. It has exactly two factors (1 and 2), which is the definition of prime. Every other even number can be divided by 2, so they have more than two factors.
Tips for Parents
- Use the "Sieve of Eratosthenes" on a 1-100 grid: cross out multiples of 2 (except 2), then 3, then 5, then 7. The numbers left are all primes. It is a satisfying activity.
- Test numbers together: "Is 23 prime? Can you divide it by 2? No. By 3? No. By 5? No. Then it is prime!" Make it a game.
- Learn the primes to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Knowing these helps with many other topics.
- Use factor trees: start with a composite number like 36 and split it into factor pairs until every branch ends in a prime. This builds understanding of prime factorisation.
Key Words
- Prime number — A number with exactly two factors: 1 and itself — like 2, 3, 5, 7, 11.
- Composite number — A number with more than two factors — like 12 (factors: 1, 2, 3, 4, 6, 12).
- Factor — A number that divides evenly into another — 3 is a factor of 15 because 15 ÷ 3 = 5.
- Factor pair — Two factors that multiply to make a number — 4 and 6 are a factor pair of 24.
- Prime factor — A factor that is itself a prime number — the prime factors of 12 are 2 and 3.
Where This Fits
Before this topic: Children should know their times tables, understand factors and multiples, and be able to test divisibility.
After this topic: Primes and composites lead to prime factorisation, finding highest common factors (HCF) and lowest common multiples (LCM), and simplifying fractions in Year 6.
How MathCraft Teaches This
In MathCraft, Prime & Composite Numbers is taught through the Coordinates & Statistics adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Prime & Composite Numbers with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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