A prime number is a number with exactly two factors, itself and 1. Almost all prime numbers are also odd. The exception is 2 which is even but also a prime number.
The table to the left highlights all the prime numbers between 1 and 100.
Any number can broken down into its prime factors. A good way to do this is to make a factor tree, then the number can be written as a prime factorisation, for example:
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Summary/Background
A factor is a whole number that divides exactly into another number. A prime number is a number with only two factors: itself and 1. The first prime numbers are 2, 3, 5, 7, 11, 13...The diagram on the right is a factor tree, showing the prime factors of 12 to be 2 and 3. Notice that 12 = 2 x 2 x 3. In this way 12 has been expressed as a product of its prime factors.
Software/Applets used on this page
Glossary
factorisation
The process of expressing a term as a product of factors.
function
A rule that connects one value in one set with one and only one value in another set.
prime
a positive integer which is divisible only by itself and 1
speed
velocity without direction; a scalar quantity
tree
A connected graph with no cycles.
union
The union of two sets A and B is the set containing all the elements of A and B.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic |
|---|---|---|---|
| AQA GCSE (9-1) Foundation (UK) | N: Structure and Calculation | N4: Factors and Multiples | Prime Numbers |
| CBSE X (India) | Number Systems | Real Numbers | Fundamental theorem of arithmetic |
| CIE IGCSE (9-1) Maths (0626 UK) | 1 Number | B1.1 Understanding Numbers | Prime Numbers |
| Edexcel GCSE (9-1) Foundation (UK) | N: Structure and Calculation | N4: Factors and Multiples | Prime Numbers |
| GCSE Foundation (UK) | Number | Arithmetic | Prime numbers |
| OCR GCSE (9-1) Foundation (UK) | 1: Number Operations and Integers | 1.02b: Prime Numbers | Prime Numbers |
| Universal (all site questions) | A | Arithmetic | Prime numbers |