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:

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

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

**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 | Exam Year |
---|---|---|---|---|

GCSE Foundation (UK) | Number | Arithmetic | Prime numbers | - |

Universal (all site questions) | A | Arithmetic | Prime numbers | - |

CBSE X (India) | Number Systems | Real Numbers | Fundamental theorem of arithmetic | - |

AQA GCSE (9-1) Foundation (UK) | N: Structure and Calculation | N4: Factors and Multiples | Prime Numbers | - |

OCR GCSE (9-1) Foundation (UK) | 1: Number Operations and Integers | 1.02b: Prime Numbers | Prime Numbers | - |

Edexcel GCSE (9-1) Foundation (UK) | N: Structure and Calculation | N4: Factors and Multiples | Prime Numbers | - |

CIE IGCSE (9-1) Maths (0626 UK) | 1 Number | B1.1 Understanding Numbers | Prime Numbers | - |