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Definition of factor : 1. A steward or bailiff of an estate.
2. One of the elements or quantities which, when multiplied together, from a product.
3. One of the elements, circumstances, or influences which contribute to produce a result; a constituent.
4. One who transacts business for another; an agent; a substitute; especially, a mercantile agent who buys and sells goods and transacts business for others in commission; a commission merchant or consignee. He may be a home factor or a foreign factor. He may buy and sell in his own name, and he is intrusted with the possession and control of the goods; and in these respects he differs from a broker.
5. To resolve ( a quantity) into its factors.

Synonyms:

procurator, factor out, metrication, federal agent, base, estimate, assess, prove, graduation, cistron, geocentric, means, constant, doer, circumstance, agentive role, administrator, count, common multiple, measure, gradation, aspect, assignee, operator, quality, absolute, factor in, particular, reckon, minister, detail, grammatical constituent, add up, promoter, Arabic numeral, facet, property, component part, envoy, fixings, computation, project, steward, calculate, nature, commissary, peculiarity, arithmetic progression, real, determine, gene, rep, compute, metric, fact, chemical element, integrant, performer, building block, imperial, calibration, common factor, mover

elicitation, motivator, grounds, evocation, action, inspiration, force, enforcement, determinant, compunction, root, origination, mainspring, stimulus, cause, drive, execution, effectuation, motive, source, provocation, compulsion, basis, generation

deputy, middleman, instrument, actor, broker, liaison, appointee, go-between, delegate, intermediary, operative, executor, representative, ombudsman, agent, lieutenant, emissary, mediator, agency, surrogate, substitute, proxy, vehicle, impresario, attorney, alternate, auxiliary, second

fragment, matter, component, percentage, piece, medium, filament, material, section, constituent, ingredient, member, portion, feature, part, segment, element, article, item

exponent, integral, increment, multiple, dividend, coefficient, minuend, cube root, cube, quotient, formula, divisor, arithmetic, multiplicand, radix, reciprocal, fraction, modulus, algebra, geometry, algorithm, multiplier, multiplicator, numerator, power, index, quadratics, denominator, subtrahend, square root, calculus, differential calculus, logarithm, trigonometry, antilogarithm

purify, reduce, elucidate, clarify, refine, strip, simplify

Usage examples:

• Sanchia bestowed upon the girl a long searching look; it may have suggested itself to Sanchia's open mind at that instant that Helen was likely to prove a more troublesome factor than she had counted on. - "The Desert Valley", Jackson Gregory.
• The tunnel added a new and puzzling factor to the problem already before me, and I was eager for an opportunity to sit down in peace and comfort to study the situation. - "The House of a Thousand Candles", Meredith Nicholson.
• Again the doubtful factor is the possibility for further discoveries. - "The Economic Aspect of Geology", C. K. Leith.