Divisibility
Pronunciation: /dɪˌvɪz.əˈbɪl.ɪ.ti/ Explain
An integer i is divisible by
another integer j if, when i is divided by
j, there is no remainder. For example, 12 is divisible
by 3 since 12÷3 = 4 with a remainder of 0. In formulas, divisibility is written with
a vertical bar |. For example,
write 3|12 and say "3 divides 12". If j divides
i, j is also a
factor
of i.
Properties of divisors
For integers a, b, c, m, n, p and q:
- If a|b and a|c then a|(b+c) and a|(mb+mc).
If a|b then there exists an integer p such that
a·p = b. Similarly, there exists an integer q
such that a·q = c.
- If a|b and a|c then a|c.
- If a|b and b|a then a = b or a = -b.
References
- McAdams, David E.. All Math Words Dictionary, divisibility. 2nd Classroom edition 20150108-4799968. pg 65. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 70-75. Thomson, Brooks/Cole. 2005. Last Accessed 7/3/2018. Buy the book
Cite this article as:
McAdams, David E. Divisibility. 3/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/divisibility.html.
Revision History
3/11/2019: Added clarifying wording. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
5/5/2011: Initial version. (
McAdams, David E.)