Abstract
We are so used to working with the natural numbers from infancy onwards that we take it for granted that natural numbers may be factorised uniquely into prime numbers. For example, \(360=2^{3}3^{2}5\) is the prime factorisation of 360. However, we should notice that there are already senses in which this factorisation is not really unique; we can write \(360=2\times 3\times 5\times 2\times 3\times 2\), or even \(360=(-2)\times 5\times 3\times (-3)\times 2\times 2\). Nevertheless, we can see that all these factorisations are “essentially the same”, in a way which we could make precise, and we will do so later.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Jarvis, F. (2014). Unique Factorisation in the Natural Numbers. In: Algebraic Number Theory. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-07545-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-07545-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07544-0
Online ISBN: 978-3-319-07545-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)