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
b | 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. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/d/divisibility.html.
Revision History
4/20/2019: Updated equations and expressions to the new format (
McAdams, David E.)
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.)