factors
factors — 名詞
- factorssingular
- factorsesplural
1. the things that play a part in shaping a result, decision, or situation — for ex
因素；要素
影響結果的事物或情況
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.
選擇學校時，家長通常會將地點、費用和教學品質視為關鍵因素。
collocation: key factors
Weather and soil quality are important factors for growing healthy crops.
天氣和土壤品質是種植健康作物的重要因素。
collocation: important factors
Several factors led to the team's defeat, including injuries and poor preparation.
多項因素導致球隊落敗，包括傷兵和準備不足。
factors + led to + result
The main factors behind the company's success were hard work and smart planning.
這家公司成功的主要因素是勤奮工作和明智的規劃。
factors + behind + outcome
Economic factors such as inflation and unemployment affect people's daily lives.
通貨膨脹和失業等經濟因素影響著人們的日常生活。
- 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
文法句型
factors + in + noun phrase
key/major/important + factor + in + noun phrase
用法筆記
Often modified by adjectives such as key, major, important, contributing, or deciding to show how much influence the factor has.
常見錯誤
2. whole numbers that divide exactly into another number, or that can be multiplied
因數
可整除另一數字的整數
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.
12 的因數有 1、2、3、4、6 和 12。
factors + of + number
In math class, Sora learned how to find all the factors of a large number by testing each smaller number.
在數學課上，Sora 學會了如何逐一測試較小的數字來找出一個大數的所有因數。
Two and seven are factors of fourteen because two times seven equals fourteen.
2 和 7 是 14 的因數，因為 2 乘以 7 等於 14。
demonstrates multiplication relationship
The teacher asked the class to list the common factors of 24 and 36.
老師要求全班列出 24 和 36 的公因數。
collocation: common factors
In her homework, Yuki listed the prime factors of 30 as 2, 3, and 5.
Yuki 在作業中列出了 30 的質因數：2、3 和 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
文法句型
factors + of + number
common factors + of + numbers
用法筆記
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.
常見錯誤
3. a particular level or degree on a scale that measures a quality — for example, t
係數
測量系統中的特定等級
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.
這瓶防曬乳的防曬係數為 50，可以阻擋大部分紫外線。
collocation: protection factor + of + number
The wind-chill factor made the temperature feel much colder than the thermometer showed.
風寒係數讓體感溫度比溫度計顯示的冷得多。
compound noun: wind-chill factor
Heloísa chose a moisturiser with a high SPF factor for her trip to the beach.
Heloísa 去海灘旅行時選擇了一款高防曬係數的保濕霜。
The sun protection factor on the bottle tells you how long the cream will shield your skin.
瓶子上的防曬係數告訴你這瓶乳霜能保護皮膚多久。
- protection factor
- sun protection factor
- wind-chill factor
- SPF factor
文法句型
protection + factor
sun protection + factor
wind-chill + factor
用法筆記
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).
常見錯誤
4. a multiplier that expresses the degree of proportional change in a quantity — a
倍率
表示倍數增減的數值
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.
這座城市的人口在過去五十年間增加了三倍。
by a factor of + number (increase)
The new processor runs faster by a factor of ten compared to the old model.
新處理器的運行速度比舊型號快了十倍。
Carbon dioxide levels increased by a factor of two since the industrial revolution.
工業革命以來，二氧化碳濃度增加了兩倍。
by a factor of + number (environmental context)
Imran calculated that his investment had grown by a factor of four over the decade.
Imran 計算出他的投資在十年間增長了四倍。
Reducing the cost by a factor of five would make the project much more affordable.
將成本降低五倍會讓這個專案變得可行得多。
- 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
文法句型
by a factor + of + number
increase/grow + by a factor + of + number
reduce/decrease + by a factor + of + number
用法筆記
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.
常見錯誤
factors — 動詞
- 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
影響
成為影響結果的因素之一
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.
幾個錯誤影響了團隊未能贏得合約。
factor + into + result
Poor sleep factors heavily into the low test scores of many university students.
睡眠不足是許多大學生考試成績偏低的重要原因。
factor + heavily + into
The rising cost of raw materials factored into the bakery's decision to raise prices.
原物料成本上漲影響了這家麵包店漲價的決定。
Asher's positive attitude factored greatly in his promotion to store manager.
Asher 積極的態度對他晉升為店經理有很大的幫助。
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'
文法句型
factor + into + noun phrase
用法筆記
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.
常見錯誤
2. to break a number or algebraic expression down into the smaller numbers or symbo
分解因數
將數字分解成因數
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.
學生們在代數課上學習如何分解二次方程式。
factor + [mathematical object]
Lukas factored the number 48 into 6 and 8, then further into 2, 3, 2, and 4.
Lukas 將 48 分解為 6 和 8，再進一步分解為 2、3、2 和 4。
factor + into + smaller parts
The teacher showed the class how to factor the expression x² − 9 into (x − 3)(x + 3).
老師向全班示範如何將 x² − 9 分解為 (x − 3)(x + 3)。
To simplify the fraction, first factor both the top and bottom numbers.
要化簡這個分數，先將分子和分母分別分解因數。
- 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
文法句型
factor + number/expression
factor + noun phrase + into + noun phrase
用法筆記
This is a technical mathematics term. In British English, 'factorise' (spelled with an 's') is more common than 'factor' for this sense.
常見錯誤
3. to include a particular piece of information or issue when you calculate, plan,
納入考量
將某因素納入計算或考量
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.
我們需要將運費納入總預算中。
factor + [cost] + into + [plan]
The travel time should be factored in when planning the conference schedule.
安排會議行程時，應將交通時間納入考量。
passive: be factored in
Ezra forgot to factor the sales tax into his price estimate for the client.
Ezra 忘了將營業稅納入他給客戶的報價估算中。
When hiring new staff, managers must factor the cost of training into their decisions.
招募新員工時，主管必須將培訓成本納入決策考量。
The design team factored the possibility of strong earthquakes into the building plans.
設計團隊將發生強震的可能性納入了建築規劃中。
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
文法句型
factor + noun phrase + in
factor + noun phrase + into + noun phrase
be factored + in/into
用法筆記
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.
常見錯誤
4. to leave something out of a calculation or consideration because it does not ref
排除
將某因素排除在計算之外
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.
一次性支出已從年度預算報告中排除。
passive: be factored out of
To see the real trend, you need to factor out the seasonal changes in monthly sales.
要看出真正的趨勢，你必須排除每月銷售額中的季節性變化。
factor out + [distorting element]
The researcher factored out data from participants who did not complete the survey.
研究人員排除了未完成問卷的參與者的數據。
When comparing rental prices, factor the utility bills out of the total cost.
比較租金時，將水電費從總費用中排除。
- 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
文法句型
factor + noun phrase + out
factor + noun phrase + out of + noun phrase
be factored + out
用法筆記
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).
常見錯誤
同根字
常見搭配
常用片語
- by a factor of
- factor in
- factor into
- factor out