NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ1093381
Record Type: Journal
Publication Date: 2013
Pages: 8
Abstractor: ERIC
ISSN: ISSN-0819-4564
Extending Greatest Common Divisors across the Rationals
Boudreaux, Grant; Beslin, Scott
Australian Senior Mathematics Journal, v27 n2 p55-62 2013
The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number and Algebra. The senior secondary curriculum makes no specific mention of "greatest common divisor," but the article is nevertheless a good resource for revisiting with students at this level the concepts of greatest common divisor and "lowest common multiple" in greater depth, and with a view to critical thinking. Certain concepts and problems can be used even in post-secondary instruction. In particular, teachers may find it useful in designing projects for guided self-discovery or collaborative learning. The article is written as a hybrid: part guided discovery, and part exposition of interesting results and applications. Teachers who enjoy factorisation of positive integers and the concepts of divisor and multiple will hopefully find this content useful and meaningful in making connections of those concepts with fractional numbers. Sample problems and exercises are presented at the end of the article as self-tests and as vehicles for student investigations.
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Tests/Questionnaires; Reports - Evaluative
Education Level: Secondary Education; Grade 6; Intermediate Grades; Middle Schools; Elementary Education; Grade 7; Junior High Schools
Audience: Teachers; Students
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia
Grant or Contract Numbers: N/A