Mathematics. a number or quantity placed (generally) before and multiplying another quantity, as 3 in the expression 3x.
Physics. a number that is constant for a given substance, body, or process under certain specified conditions, serving as a measure of one of its properties: coefficient of friction.
acting in consort; cooperating.

1655–65; < Neo-Latin coefficient- (stem of coefficiēns). See co-, efficient

coefficiently, adverb Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
coefficient (ˌkəʊɪˈfɪʃənt)
1.  maths
 a.  a numerical or constant factor in an algebraic term: the coefficient of the term 3xyz is 3
 b.  the product of all the factors of a term excluding one or more specified variables: the coefficient of x in 3axyz is 3ayz
2.  physics a value that relates one physical quantity to another
[C17: from New Latin coefficiēns, from Latin co- together + efficere to effect]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1660s, from co- + efficient, probably influenced by Mod.L. coefficiens, used in mathematics 16c.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Medical Dictionary

coefficient co·ef·fi·cient (kō'ə-fĭsh'ənt)
The mathematical expression of the amount or degree of any quality possessed by a substance, or of the degree of physical or chemical change normally occurring in that substance under stated conditions.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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American Heritage
Science Dictionary
coefficient   (kō'ə-fĭsh'ənt)  Pronunciation Key 
  1. A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. For example, 4 is the coefficient in the term 4x, and x is the coefficient in x(a + b).

  2. A numerical measure of a physical or chemical property that is constant for a system under specified conditions. The speed of light in a vacuum, for example, is a constant.

The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
It's complicated, expensive, and produces lower validity coefficients than the
  traditional tests.
The table above lists the coefficients of correlation between size and shape of
  fingerprints found in one study.
The authors give us a hint when they point out that that these coefficients
  vary according to what kinds of foods are exploited.
The author uses correlation coefficients in sentences incorrectly, which
  suggests a poor understanding of what they are and mean.
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