Prime Numbers
A prime number has exactly two factors, itself and one, and cannot be made by multiplying smaller whole numbers.
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A prime number has exactly two factors, itself and one, and cannot be made by multiplying smaller whole numbers.
- The first primes are 2, 3, 5, 7, 11 and 13
- Two is the only even prime
- One is not prime because it has just one factor
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Prime Numbers?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Prime Numbers. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Prime Numbers in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Prime Numbers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Prime Numbers in detail
A prime number has exactly two factors, 1 and itself, so 2, 3, 5, 7, 11 and 13 are prime while 1 is not prime because it has only one factor. Two is the only even prime, because every other even number is divisible by 2.
Primes are the building blocks of all whole numbers, since every integer greater than 1 is either prime or can be written as a product of primes. To test whether a number is prime, check divisibility by primes up to its square root. Primes also protect online data, as modern encryption relies on how hard it is to factorise very large numbers.
How the interactive helps you understand Prime Numbers
Click a step, or use the Previous and Next buttons, to move through the sequence one stage at a time. Auto-play moves on for you.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Prime Numbers.
Real-life uses and examples
- Check a homework answer about Prime Numbers by estimating first, then working it out step by step.
- Use Prime Numbers when comparing prices, discounts or recipe quantities in everyday life.
- Explain Prime Numbers to a friend with a simple picture, such as a row of tiles or a bag of sweets.
Common mistakes to avoid
- Memorising the steps for Prime Numbers without checking why they work.
- Forgetting units, signs or brackets when you apply Prime Numbers.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Prime Numbers
What is Prime Numbers?
A prime number has exactly two factors, itself and one, and cannot be made by multiplying smaller whole numbers.
What are the most important points about Prime Numbers?
The main points are: The first primes are 2, 3, 5, 7, 11 and 13; Two is the only even prime; One is not prime because it has just one factor.
Why is Prime Numbers useful?
Understanding Prime Numbers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Prime Numbers?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Prime Numbers?
Related topics in Mathematics include Lowest Common Multiple, Negative Numbers, Adding and Subtracting Fractions.