factors
factors — noun
- factorssingular
- factorsesplural
1. the things that play a part in shaping a result, decision, or situation — for ex
the things that play a part in shaping a result, decision, or situation — for example, the weather being a factor in a farmer's harvest, or cost being a factor in choosing a place to live.
When choosing a school, parents often consider location, cost, and teaching quality as key factors.
collocation: key factors
Weather and soil quality are important factors for growing healthy crops.
collocation: important factors
Several factors led to the team's defeat, including injuries and poor preparation.
factors + led to + result
The main factors behind the company's success were hard work and smart planning.
factors + behind + outcome
Economic factors such as inflation and unemployment affect people's daily lives.
- key factor
- major factor
- important factor
- contributing factor
- deciding factor
- factor in
- factor behind
- element
more neutral; an element is simply a part of something, not necessarily one that drives the result
- influence
emphasises the power to change or shape an outcome rather than being one of many pieces
- consideration
focuses on something that is thought about before a decision rather than something that actively causes a result
Grammar Patterns
factors + in + noun phrase
key/major/important + factor + in + noun phrase
Usage Note
Often modified by adjectives such as key, major, important, contributing, or deciding to show how much influence the factor has.
Common Mistakes
2. whole numbers that divide exactly into another number, or that can be multiplied
whole numbers that divide exactly into another number, or that can be multiplied together to give that number — for example, 2 and 6 are factors of 12 because 2 × 6 = 12.
Look at the number twelve — its factors are 1, 2, 3, 4, 6, and 12, which all divide it evenly.
factors + of + number
In math class, Sora learned how to find all the factors of a large number by testing each smaller number.
Two and seven are factors of fourteen because two times seven equals fourteen.
demonstrates multiplication relationship
The teacher asked the class to list the common factors of 24 and 36.
collocation: common factors
In her homework, Yuki listed the prime factors of 30 as 2, 3, and 5.
concrete scene: named person + prime factors of a specific number
- common factor
- prime factor
- factor of
- list the factors
- find the factors
- product
the result of multiplying factors, not the factors themselves
Grammar Patterns
factors + of + number
common factors + of + numbers
Usage Note
In everyday math, the phrase 'common factors' refers to numbers that divide two or more numbers exactly. 'Prime factors' are factors that are also prime numbers.
Common Mistakes
3. a particular level or degree on a scale that measures a quality — for example, t
a particular level or degree on a scale that measures a quality — for example, the sun protection factor on sunscreen tells you how well it blocks UV light.
This sunscreen has a protection factor of 50, which blocks most UV rays.
collocation: protection factor + of + number
The wind-chill factor made the temperature feel much colder than the thermometer showed.
compound noun: wind-chill factor
Heloísa chose a moisturiser with a high SPF factor for her trip to the beach.
The sun protection factor on the bottle tells you how long the cream will shield your skin.
- protection factor
- sun protection factor
- wind-chill factor
- SPF factor
Grammar Patterns
protection + factor
sun protection + factor
wind-chill + factor
Usage Note
The word 'factor' alone in this sense usually appears as part of a compound noun (sun protection factor, wind-chill factor) or as part of a technical label (SPF factor is sometimes considered redundant but is common in everyday language).
Common Mistakes
4. a multiplier that expresses the degree of proportional change in a quantity — a
a multiplier that expresses the degree of proportional change in a quantity — a threefold price rise uses three as this value.
The population of the city has grown by a factor of three in the last fifty years.
by a factor of + number (increase)
The new processor runs faster by a factor of ten compared to the old model.
Carbon dioxide levels increased by a factor of two since the industrial revolution.
by a factor of + number (environmental context)
Imran calculated that his investment had grown by a factor of four over the decade.
Reducing the cost by a factor of five would make the project much more affordable.
- by a factor of
- factor of
- increase by a factor
- decrease by a factor
- reduce by a factor
- multiple
similar meaning in maths contexts; 'by a multiple of' is also used but 'by a factor of' is more common
- multiplier
emphasises the number doing the multiplying rather than the resulting size difference
Grammar Patterns
by a factor + of + number
increase/grow + by a factor + of + number
reduce/decrease + by a factor + of + number
Usage Note
Almost always used in the fixed phrase 'by a factor of + number'. The number must be a whole number or decimal — 'by a factor of half' is not idiomatic; use 'by half' instead.
Common Mistakes
factors — verb
- factorspresent simple I / you / we / they
- factorses3rd person singular
- factorsing-ing form
- factorsedpast simple
1. to be one of the causes that help bring about a particular outcome — for example
to be one of the causes that help bring about a particular outcome — for example, when a lack of sleep factors into a student getting low grades.
Several mistakes factored into the team's failure to win the contract.
factor + into + result
Poor sleep factors heavily into the low test scores of many university students.
factor + heavily + into
The rising cost of raw materials factored into the bakery's decision to raise prices.
Asher's positive attitude factored greatly in his promotion to store manager.
factor + greatly + in
- factor into
- factor in
- factor heavily
- factor greatly
- contribute to
more direct and widely understood; 'factor into' is slightly more formal and commonly used in business writing
- play a part in
less formal, more conversational than 'factor into'
Grammar Patterns
factor + into + noun phrase
Usage Note
Almost always used with 'into' (American English) or 'in' (more common in informal contexts). The subject is typically a situation, condition, or mistake — not a person.
Common Mistakes
2. to break a number or algebraic expression down into the smaller numbers or symbo
to break a number or algebraic expression down into the smaller numbers or symbols that multiply together to give it — for example, factoring 12 into 3 and 4, or x² − 9 into (x − 3)(x + 3).
The students learned how to factor quadratic equations in their algebra class.
factor + [mathematical object]
Lukas factored the number 48 into 6 and 8, then further into 2, 3, 2, and 4.
factor + into + smaller parts
The teacher showed the class how to factor the expression x² − 9 into (x − 3)(x + 3).
To simplify the fraction, first factor both the top and bottom numbers.
- factor an equation
- factor an expression
- factor into
- factor completely
- factorise
British variant spelling; equally common in UK math textbooks
- break down
more general term that works in non-technical contexts but lacks the precision of 'factor'
- multiply
the reverse operation — multiplying factors produces the original number or expression
Grammar Patterns
factor + number/expression
factor + noun phrase + into + noun phrase
Usage Note
This is a technical mathematics term. In British English, 'factorise' (spelled with an 's') is more common than 'factor' for this sense.
Common Mistakes
3. to include a particular piece of information or issue when you calculate, plan,
to include a particular piece of information or issue when you calculate, plan, or make a decision — for example, factoring the cost of fuel into a travel budget.
We need to factor the cost of shipping into our total budget.
factor + [cost] + into + [plan]
The travel time should be factored in when planning the conference schedule.
passive: be factored in
Ezra forgot to factor the sales tax into his price estimate for the client.
When hiring new staff, managers must factor the cost of training into their decisions.
The design team factored the possibility of strong earthquakes into the building plans.
factor + risk + into + plan
- factor in
- factor into
- be factored in
- factor the cost
- factor the risk
- take into account
more general and can be used in any context; 'factor in' is more common in quantitative or planning situations
- include
simpler but does not carry the weight of careful consideration that 'factor in' suggests
- factor out
the direct opposite — to intentionally leave something out of the calculation or decision
Grammar Patterns
factor + noun phrase + in
factor + noun phrase + into + noun phrase
be factored + in/into
Usage Note
Common in business, finance, and project planning. The object is usually a cost, risk, time, or condition. The particle 'in' or 'into' is required — 'factor the cost' alone is incomplete.
Common Mistakes
4. to leave something out of a calculation or consideration because it does not ref
to leave something out of a calculation or consideration because it does not reflect the normal situation — for example, factoring out one-time sales to see regular monthly trends.
One-time expenses were factored out of the annual budget report.
passive: be factored out of
To see the real trend, you need to factor out the seasonal changes in monthly sales.
factor out + [distorting element]
The researcher factored out data from participants who did not complete the survey.
When comparing rental prices, factor the utility bills out of the total cost.
- factor out
- factor out of
- be factored out
- factor out the effects
- exclude
simpler and more general; 'factor out' adds a sense of deliberate removal for analytical clarity
- isolate
focuses on separating one element to examine it, rather than removing it entirely
- remove from consideration
more formal phrasing used in decision-making contexts
- factor in
the direct opposite — to include an element in the calculation or decision
Grammar Patterns
factor + noun phrase + out
factor + noun phrase + out of + noun phrase
be factored + out
Usage Note
Opposite of 'factor in'. Frequently used in data analysis, research, and budgeting to remove variables that would distort the main picture. The object is typically something unwanted or exceptional (outliers, one-off costs, seasonal effects).
Common Mistakes
Word family
Synonym discussion
Sense: noun/1
All four words describe something that plays a part in a situation or decision, but they differ in emphasis. A 'factor' is something that actively and measurably contributes to a result — for example, 'Cost was the deciding factor in choosing a supplier.' An 'element' is simply a part or component of a larger whole, without the implication of causation: 'Honesty is an important element of a good relationship.' 'Influence' stresses the power to change or shape an outcome, often in a subtle or gradual way: 'Her teacher's encouragement had a strong influence on her career choice.' 'Consideration' focuses on something that is deliberately thought about before a decision, rather than something that actively causes an outcome: 'Safety was a key consideration in the design process.' In practice, 'factor' and 'consideration' overlap most when discussing decisions — the difference is that a 'factor' drives the result, while a 'consideration' is simply weighed.
Common collocations
Phrases
- by a factor of
- factor in
- factor into
- factor out
Etymology
The word 'factor' comes directly from Latin 'factor', meaning 'maker, doer', which comes from 'facere' meaning 'to do, to make'. It entered English in the 1400s with the sense of 'a person who acts for another' (an agent or deputy). The mathematical meaning — a number that divides another number exactly — appeared in the 1600s. The general sense of 'an element that contributes to a result' developed in the 1800s and is now the most common everyday use.
First known use
15th century
15th century, in the meaning defined at sense 1 Verb