Prime numbers
Objective. Recognise primes and distinguish them from composite numbers.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A prime number is a whole number greater than 1 with exactly two factors: 1 and itself. For instance, 7 is prime because only 1 and 7 divide into it exactly. A composite number has more than two factors, such as 8, whose factors are 1, 2, 4 and 8. To test whether a number is prime, try dividing it by each prime up to its square root; if none divide exactly, it is prime. The number 1 is neither prime nor composite, since it has only one factor. The first few primes are 2, 3, 5, 7, 11 and 13.
Worked example
Which of these numbers is prime: 21, 29, 33, 35?
- 21
- 29
- 33
- 35
- 1Test 21: 21=3×7, so it is composite.
- 2Test 29: no prime up to √29≈5.4 (2, 3, 5) divides it exactly.
- 3Test 33 and 35: 33=3×11 and 35=5×7, both composite.
- 4Only 29 has exactly two factors.
Answer: 29
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Practice
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Start practisingCommon mistake. Pupils often think all odd numbers are prime, wrongly including 9 or 15. Check every odd number against small primes like 3 and 5 before deciding, since 9=3×3 and 15=3×5 are composite.
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