Prime Numbers
A prime has exactly two positive divisors: 1 and itself.
Key idea
A prime has exactly two positive divisors: 1 and itself.
In depth
A prime has exactly two factors: 1 and itself. Primes are the building blocks of all whole numbers. 2 is the only even prime. To test a number, check divisibility only by primes up to its square root.
Worked example
Is 29 prime? √29 ≈ 5.4; test 2, 3, 5: none divide it. So 29 is prime.
Formula
Real-world uses
- Generating keys in cryptography
- Splitting things into equal groups that cannot be made smaller
Common mistake
Calling 1 prime. It has only one factor, so it is neither prime nor composite.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Prime Numbers?
A prime has exactly two positive divisors: 1 and itself. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Prime Numbers?
The key formula is 2, 3, 5, 7, 11, 13, ….
Where is Prime Numbers used in real life?
Real-world examples: Generating keys in cryptography; Splitting things into equal groups that cannot be made smaller.
What should I learn before Prime Numbers?
Make sure you are comfortable with Divisibility Rules, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Prime Numbers?
Calling 1 prime. It has only one factor, so it is neither prime nor composite.
How can I practise Prime Numbers?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Prime Numbers?
Move on to Composite Numbers next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Composite Numbers – Numbers greater than 1 with more than two factors.
- Prime Factorization – Every integer above 1 is a unique product of primes.