factor
factor — 名詞
1. a condition, quality, or event that helps bring about a particular outcome, ofte
因素
影響結果或情況的條件或事件
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.
高額的房租是他們決定搬到小城鎮的一個主要因素。
major factor in [decision/result]
Ayesha listed three key factors that helped her company grow so quickly last year.
Ayesha 列出了三個幫助她公司去年快速成長的關鍵因素。
key factor
Poor sleep is often a contributing factor in workplace accidents and injuries.
睡眠不足往往是職場事故和受傷的促成因素之一。
When buying a house, location was the most important factor for the Watanabe family.
買房子時，地點對 Watanabe 家來說是最重要的因素。
Scientists are studying the environmental factors that affect coral reef health.
科學家正在研究影響珊瑚礁健康的環境因素。
- 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
文法句型
factor + in + noun phrase
factor + behind + noun phrase
用法筆記
Commonly modified by adjectives such as key, major, contributing, decisive, and risk. The preposition in often introduces the result or situation affected.
常見錯誤
2. a whole number that divides exactly into another number; a number that can be mu
因數
可整除另一整數的數
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.
數字 12 有六個因數：1、2、3、4、6 和 12。
In today's class, the students learned to find the prime factors of 30.
今天的課堂上，學生們學習找出 30 的質因數。
prime factors
Three and five are factors of fifteen because three times five equals fifteen.
三和五是十五的因數，因為三乘以五等於十五。
Kian explained that the greatest common factor of 18 and 24 is 6.
Kian 解釋說，18 和 24 的最大公因數是 6。
A factor tree helps students break a number into its prime factors step by step.
因數樹可以幫助學生一步一步將數字分解成質因數。
- 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
文法句型
factor + of + number
prime factor
common factor
用法筆記
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.
常見錯誤
3. a numerical value on a measurement scale that indicates the degree or level of a
係數；等級
測量尺度上的數值
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.
Élise 去海邊時總是使用防曬係數很高的防曬乳。
sun protection factor (SPF)
The building's insulation factor was tested during the extremely cold winter months.
這棟建築的隔熱係數在最寒冷的冬天接受了檢測。
Scientists measured the cooling factor of several new materials in the laboratory.
科學家在實驗室裡測量了幾種新材料的冷卻係數。
A car's drag factor affects how much fuel it uses while driving on the highway.
汽車的風阻係數會影響它在高速公路上行駛時的油耗。
The wind chill factor made the temperature feel much colder than the thermometer showed.
風寒效應讓實際體感溫度比溫度計顯示的數值還要冷得多。
- 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
文法句型
[noun] + factor
factor of [noun]
用法筆記
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
倍數；倍率
表示增減倍數的數值
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.
這家公司的利潤在過去五年裡成長了四倍。
by a factor of [number] — multiplier pattern
The new software made the data processing speed faster by a factor of ten.
這套新軟體讓資料處理速度加快了十倍。
Hyun's heating bills increased by a factor of three after the unusually long winter.
Hyun 的暖氣費用在異常漫長的冬天之後增加了三倍。
The earthquake reduced the city's available water supply by a factor of five.
地震使該市的可用供水減少了五分之四。
Olivia's commute time rose by a factor of two after the bridge closed.
Olivia 計算出她的通勤時間自那座橋關閉後已經變成了原來的兩倍。
- multiple
similar meaning, but 'multiple' focuses on the result, while 'factor' focuses on the multiplier itself
文法句型
by a factor of + number
用法筆記
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.
常見錯誤
factor — 動詞
1. to break a number or algebraic expression into its component factors, typically
因數分解
將數字或代數式分解成因數
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.
在代數課上，學生們學會了自己將二次方程式做因數分解。
Femi showed the class how to factor the expression into two binomials.
Femi 向全班示範如何將該代數式分解成兩個二項式。
factor [expression] into [parts]
The teacher asked the students to factor the number 36 completely on the worksheet.
老師要求學生在學習單上將數字 36 完全分解。
You can factor this polynomial by grouping the terms in pairs first.
你可以先把項次兩兩分組，再對這個多項式進行因數分解。
文法句型
factor + noun phrase (number/expression)
factor + noun phrase + into + noun phrase
用法筆記
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
納入考慮
在決策時將…列入考量
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.
在規劃預算時，我們需要把聘用新員工的成本納入考慮。
factor in [something]
Ramón factored the weather conditions into his travel plans before booking the flight.
Ramón 在預訂航班之前，已將天氣狀況列入旅行規劃中考量。
factor [something] into [something]
The committee failed to factor in the extra time needed for public feedback.
委員會未能將公眾意見回饋所需的額外時間納入考慮。
Parents should factor childcare expenses into their monthly budget calculations.
父母應該將托兒費用列入每月的預算計算中。
Sirin always factors the morning traffic into her commute time estimate.
Sirin 規劃通勤時間時，總是會把早上的交通狀況納入考量。
- 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'
文法句型
factor in + noun phrase
factor + noun phrase + into + noun phrase
用法筆記
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.
常見錯誤
3. to deliberately remove or not include a particular factor when thinking about or
排除
在決策或計算時將…排除
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.
為了公平比較，研究人員排除了各組之間的年齡差異。
factor out [something] — exclude from analysis
Hugo factored out the one-time costs when calculating the annual budget figures.
Hugo 在計算年度預算數字時，排除了那些一次性費用。
The study factored out patients with pre-existing health conditions from the results.
這項研究從結果中排除了有既有健康狀況的患者。
When comparing job offers, factor out location differences and focus on salary.
在比較兩份工作機會時，你應該排除地點差異，專注在薪資上。
- 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
文法句型
factor out + noun phrase
factor + noun phrase + out
用法筆記
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.
常見錯誤
4. to be one of the causes or conditions that combine to produce a particular outco
促成；導致
成為造成某結果的因素之一
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.
根據報告，好幾個問題促成了該專案上季的失敗。
factor into [result]
His lack of experience factored heavily in the committee's final hiring decision.
他缺乏經驗這點，在委員會的最終招聘決定中占了很大因素。
The rising cost of raw materials factored into the company's decision to raise prices.
原物料成本上漲是該公司決定調漲價格的原因之一。
Both hard work and luck factored into Lauren's success as a restaurant chef.
努力和運氣共同促成了 Lauren 成為一名餐廳主廚的成功。
The new teacher's enthusiasm factored heavily in the students' improved test scores.
新老師的教學熱忱是學生考試成績進步的重要原因之一。
- 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'
文法句型
factor into + noun phrase
factor in + noun phrase
用法筆記
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.