Exploring the fundamental theorem of arithmetic in Excel 2007

Stephen Sugden, Bond University
David Miller, West Virginia University

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Published Version.

Sugden, S., & Miller, D. (2010). Exploring the fundamental theorem of arithmetic in Excel 2007. Spreadsheets in Education, 4(2), 1-27.

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2010 HERDC submission. FoR Code: 019900

© Copyright Stephen Sugden & David Miller, 2010

Abstract

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.