lesson
Sort numbers by their factors
1 · Learn
A factor divides a whole number exactly. A prime number has exactly two positive factors: 1 and itself. A composite number has more than two. One is neither prime nor composite.
The primes up to 19 are 2, 3, 5, 7, 11, 13, 17 and 19. Two is the only even prime; other even numbers greater than two have 2 as another factor.
A prime factor is a factor that is itself prime. The factors of 18 are 1, 2, 3, 6, 9 and 18; its prime factors are 2 and 3. To check a number below 100 for primality, test divisibility by 2, 3, 5 and 7. Any composite number below 100 has a prime factor in that list. For 97, none divides exactly, so 97 is prime.
2 · Worked example
To test 21, I notice 3 × 7 = 21. It has factors other than 1 and itself, so it is composite.
3 · Your turn
List the common factors of 12 and 18. Is 29 prime or composite? Explain.
Check your answer
Common factors: 1, 2, 3, 6. 29 is prime: only 1 and 29 divide it exactly among positive whole numbers.
4 · Apply your learning
Build factor-pair lists and use a hundred grid to investigate prime numbers, explaining why each crossed-out number has an additional factor.
Adult guidance and safety
Model the calculation or measurement before relying on a procedure. Explain estimates, units and checks. Use a ruler/protractor and suitable diagrams where needed; text examples alone do not establish practical skill or fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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