factor
factor — noun
1. a condition, quality, or event that helps bring about a particular outcome, ofte
a condition, quality, or event that helps bring about a particular outcome, often alongside other such influences
High rent was a major factor in their decision to move to a smaller town.
major factor in [decision/result]
Ayesha listed three key factors that helped her company grow so quickly last year.
key factor
Poor sleep is often a contributing factor in workplace accidents and injuries.
contributing factor in
When buying a house, location was the most important factor for the Watanabe family.
Scientists are studying the environmental factors that affect coral reef health.
- key factor
- major factor
- contributing factor
- risk factor
- decisive factor
- determining factor
- factor in
- element
suggests a part that makes up a whole; more neutral than 'factor'
- component
implies a necessary piece of a larger system or process
- cause
stronger and more direct than 'factor'; implies a clear cause-and-effect link
- determinant
more formal; used when the influence is decisive or controlling
- result
factor leads to a result; they are opposite sides of a cause-effect relationship
- consequence
the outcome rather than the influence that produces it
Grammar Patterns
factor + in + noun phrase
factor + behind + noun phrase
Usage Note
Commonly modified by adjectives such as key, major, contributing, decisive, and risk. The preposition in often introduces the result or situation affected.
Common Mistakes
2. a whole number that divides exactly into another number; a number that can be mu
a whole number that divides exactly into another number; a number that can be multiplied by another to produce a given product
The number twelve has six factors: one, two, three, four, six, and twelve itself.
In today's class, the students learned to find the prime factors of 30.
prime factors
Three and five are factors of fifteen because three times five equals fifteen.
Kian explained that the greatest common factor of 18 and 24 is 6.
greatest common factor (GCF)
A factor tree helps students break a number into its prime factors step by step.
- prime factor
- common factor
- greatest common factor
- factor of
- factor tree
- divisor
technical synonym; more common in division contexts than multiplication
- submultiple
rare; used in formal mathematical writing
- multiple
the product of a multiplication, not the number that divides into another
Grammar Patterns
factor + of + number
prime factor
common factor
Usage Note
Distinguish from multiple: a factor divides into a number, whereas a multiple is produced by multiplication. For example, 3 is a factor of 12, and 12 is a multiple of 3.
Common Mistakes
3. a numerical value on a measurement scale that indicates the degree or level of a
a numerical value on a measurement scale that indicates the degree or level of a particular quality, often in safety or health contexts
Élise always uses sunscreen with a high sun protection factor at the beach.
sun protection factor (SPF)
The building's insulation factor was tested during the extremely cold winter months.
Scientists measured the cooling factor of several new materials in the laboratory.
A car's drag factor affects how much fuel it uses while driving on the highway.
The wind chill factor made the temperature feel much colder than the thermometer showed.
wind chill factor
- sun protection factor
- wind chill factor
- insulation factor
- power factor
- drag factor
- cooling factor
- rating
more general; a score or classification rather than a measured numerical value
- index
suggests a ratio or comparative scale; more technical
- coefficient
used in scientific contexts; often a constant multiplier in formulas
Grammar Patterns
[noun] + factor
factor of [noun]
Usage Note
This sense appears frequently in compound nouns such as SPF (sun protection factor), wind chill factor, and power factor. The noun that precedes factor names the quality being measured.
4. a multiplier that indicates the degree of change in an amount, showing for examp
a multiplier that indicates the degree of change in an amount, showing for example that it has doubled or halved
The company's profits grew by a factor of four over the past five years.
by a factor of [number] — multiplier pattern
The new software made the data processing speed faster by a factor of ten.
Hyun's heating bills increased by a factor of three after the unusually long winter.
The earthquake reduced the city's available water supply by a factor of five.
Olivia's commute time rose by a factor of two after the bridge closed.
- by a factor of
- increase by a factor of
- reduce by a factor of
- grow by a factor of
- multiple
similar meaning, but 'multiple' focuses on the result, while 'factor' focuses on the multiplier itself
Grammar Patterns
by a factor of + number
Usage Note
Almost always appears in the fixed expression by a factor of [number]. Used for both increases and decreases, though verbs like reduce or drop make clear which direction is meant.
Common Mistakes
the feel-good factor
idiomA general sense of happiness and optimism that many people share at the same time.
The team's winning streak brought back the feel-good factor among fans.
Did the new park create a feel-good factor in the neighborhood?
factor — verb
1. to break a number or algebraic expression into its component factors, typically
to break a number or algebraic expression into its component factors, typically as a step in solving a problem
In algebra class, the students learned to factor quadratic equations on their own.
Femi showed the class how to factor the expression into two binomials.
factor [expression] into [parts]
The teacher asked the students to factor the number 36 completely on the worksheet.
You can factor this polynomial by grouping the terms in pairs first.
- factor into
- factor completely
- factor a number
- factor an expression
- factor a polynomial
Grammar Patterns
factor + noun phrase (number/expression)
factor + noun phrase + into + noun phrase
Usage Note
Primarily used in mathematics education contexts. The result is usually introduced with into (e.g., factor 12 into 3 and 4).
2. to include a particular piece of information or condition as part of the reasoni
to include a particular piece of information or condition as part of the reasoning when planning or deciding something
When planning the budget, we need to factor in the cost of hiring new staff.
factor in [something]
Ramón factored the weather conditions into his travel plans before booking the flight.
factor [something] into [something]
The committee failed to factor in the extra time needed for public feedback.
Parents should factor childcare expenses into their monthly budget calculations.
Sirin always factors the morning traffic into her commute time estimate.
- factor in
- factor into
- factor something in
- factor something into
- include
simpler and more general; less precise for decision-making contexts
- take into account
slightly more formal; same meaning, cannot be shortened to one verb
- incorporate
more formal; implies active integration rather than passive inclusion
- factor out
the opposite operation: to exclude deliberately from consideration
- exclude
simpler antonym; lacks the decision-making nuance of 'factor out'
Grammar Patterns
factor in + noun phrase
factor + noun phrase + into + noun phrase
Usage Note
Commonly used as the phrasal verbs factor in (object between or after the particle) or factor into (followed directly by the situation). Both are separable: You can factor the cost in or factor in the cost.
Common Mistakes
3. to deliberately remove or not include a particular factor when thinking about or
to deliberately remove or not include a particular factor when thinking about or calculating something, so that it does not affect the result
To get a fair comparison, the researchers factored out the age differences between the groups.
factor out [something] — exclude from analysis
Hugo factored out the one-time costs when calculating the annual budget figures.
The study factored out patients with pre-existing health conditions from the results.
When comparing job offers, factor out location differences and focus on salary.
- factor out
- factor something out of
- factor out of consideration
- exclude
simpler and more direct; less idiomatic than 'factor out' for analytical contexts
- disregard
implies intentionally not considering; slightly more formal
- remove from consideration
more wordy but clearer in formal writing
Grammar Patterns
factor out + noun phrase
factor + noun phrase + out
Usage Note
Opposite of factor in. The particle out can come before or after the object (factor out the costs / factor the costs out), but when the object is long or a clause, out usually stays adjacent to the verb.
Common Mistakes
4. to be one of the causes or conditions that combine to produce a particular outco
to be one of the causes or conditions that combine to produce a particular outcome
Several problems factored into the project's failure last quarter according to the report.
factor into [result]
His lack of experience factored heavily in the committee's final hiring decision.
The rising cost of raw materials factored into the company's decision to raise prices.
Both hard work and luck factored into Lauren's success as a restaurant chef.
The new teacher's enthusiasm factored heavily in the students' improved test scores.
- factor into
- factor in
- factor heavily in
- factor into the decision
- contribute to
more general and more common than 'factor into'; can apply to positive or negative results
- play a part in
idiomatic; slightly informal
- be a factor in
a noun-based alternative using the noun sense of 'factor'
Grammar Patterns
factor into + noun phrase
factor in + noun phrase
Usage Note
Intransitive — no direct object follows. The contributing element is the subject, and the result is introduced by into or in. This sense differs from verb sense 2 (factor in) because here the subject is the influence itself, not the person including it.
Word family
- factorialnounC1
- factorizationnounC1
- factorableadjectiveC2
Synonym discussion
Sense: noun/1
All five words refer to something that plays a part in producing a result, but they differ in emphasis. Factor highlights something that actively influences an outcome, usually among several such influences — for example, cost is a factor in choosing a school. Element suggests a basic, often essential part that makes up a system: "trust is a key element of a strong relationship." Component implies a functional piece of a larger mechanism or process, such as "the brake component of a car." Cause is stronger and more direct, pointing to a clear source of an effect: "smoking is the leading cause of lung cancer." Determinant is the most formal and academic, used when the influence is decisive — "income level is a strong determinant of life expectancy." In everyday speech, factor and cause are the most common; component and determinant sound more technical.
Common collocations
Etymology
The word factor comes from Latin 'factor', meaning 'maker' or 'doer', which comes from 'facere' (to make or do). It entered English through French in the 15th century, first referring to a person who acted as an agent or deputy. The mathematical meaning appeared in the 17th century, and the broader sense of 'influence that contributes to a result' developed in the 19th century.