Unique factorization and the fundamental theorem of arithmetic. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Sprows, David
• Is Part Of: International journal of mathematical education in science and technology. Volume 48:Issue 1(2017)
• Page Start: 130
• Page End: 131
• Publication Date: 2017-01-02
• Subjects: Factorization -- prime -- abundant number; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2016.1199059
• Languages: English
• ISSNs: 0020-739X

Abstract

ABSTRACT: The fundamental theorem of arithmetic is one of those topics in mathematics that somehow 'falls through the cracks' in a student's education . When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like 'every natural number can be broken down into a product of primes'. The fact that this breakdown always results in the same primes is viewed as 'obvious'. The purpose of this paper is to illustrate with a number of examples that the 'Unique Factorization Property' is a rare property and the fact that the natural numbers possess this property is 'fundamental' to our understanding of this number system.