MathsNet: A - Arithmetic - Prime factors

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Page ID: 11528

A | Arithmetic | Prime numbers | «Prime factors»

primes table

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

factor tree

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

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This question appears in the following syllabi:

Syllabus	Module	Section	Topic	Exam Year
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	-