factorial
factorial — 名詞
1. A value that you calculate by taking a given whole number and multiplying it by
階乘
從1乘到該數的乘積
A value that you calculate by taking a given whole number and multiplying it by every smaller whole number down to 1. For example, the factorial of 5 (written as 5!) is 5 × 4 × 3 × 2 × 1 = 120.
Tariro learned from her textbook that 5 factorial, written as 5!, equals one hundred and twenty.
Tariro 從課本中學到 5 的階乘寫成 5！，等於 120。
5! notation: factorial written as number followed by exclamation mark
The computer science students wrote a short program to calculate the factorial of any number typed into the console.
電腦科學課的學生寫了一個簡短程式，用來計算輸入的任何數字的階乘。
factorial + of + number in computing context
Cyrus computed the factorial of 7 to find how many ways he could arrange seven different books on a shelf.
Cyrus 計算了 7 的階乘，才知道七本不同的書在書架上有多少種排列方式。
The factorial of 10 is 3,628,800, a value that appears often in probability and statistics problems.
10 的階乘等於三百六十二萬八千八百，這個數字經常出現在機率與統計的問題中。
- product
a more general term for the result of any multiplication; not specific to the 1-to-n operation
文法句型
factorial + of + number
用法筆記
In mathematical writing, the factorial of a number n is written as n! (read as 'n factorial'). The value grows very quickly — the factorial of 20 is already over 2.4 quintillion.
常見錯誤
factorial — 形容詞
1. Relating to the factors that affect or influence a result, especially in researc
因子的
與影響結果的因素有關的
Relating to the factors that affect or influence a result, especially in research that tests more than one variable at the same time.
The researchers used a factorial design to test how both temperature and humidity affected plant growth.
研究人員使用因子設計來測試溫度和濕度如何同時影響植物生長。
factorial design: testing two variables together
Kabir and his team applied a factorial analysis to separate the effects of age and income on consumer habits.
Kabir 和他的團隊應用了因子分析，來區分年齡和收入對消費者習慣的影響。
factorial analysis: examining multiple contributing factors
The factorial structure of the survey results revealed several distinct factors that influenced student satisfaction.
這份調查結果的因子結構顯示出幾個明顯影響學生滿意度的因素。
Gabriel set up a factorial experiment to study how light and water together affect seed germination.
Gabriel 設計了一個因子實驗，以研究光線和水分如何共同影響種子發芽。
- multiple-factor
emphasises the involvement of several variables rather than just one
- multi-variable
broader term used across statistics and engineering; less specific to experimental design
- single-variable
describes a study that tests only one factor at a time
文法句型
factorial + noun (design / analysis / structure)
用法筆記
Almost exclusively used in academic or technical research contexts, particularly experimental design and statistical analysis. The more common everyday word is 'factor' (noun), not 'factorial' (adjective).
常見錯誤
2. Relating to the mathematical operation in which a whole number is multiplied by
階乘的
與階乘運算或符號有關的
Relating to the mathematical operation in which a whole number is multiplied by every smaller positive whole number down to 1.
Astrid checked the factorial table in her textbook to find the value of 6!.
Astrid 翻閱課本中的階乘表，查詢 6！的值是多少。
factorial table: a reference list of computed factorial values
The factorial symbol is an exclamation mark placed right after a whole number, such as in 4! or 12!.
階乘的符號是一個緊貼在整數後方的驚嘆號，例如 4！或 12！。
Before solving the probability problems, the students reviewed factorial notation and how it relates to permutations.
在解機率問題之前，學生複習了階乘記號以及它與排列的關係。
Putri wrote a factorial expression for the number of possible seating arrangements of six guests at a table.
Putri 用階乘表達式來計算六位賓客在一張餐桌上的可能座位安排數。
文法句型
factorial + noun (notation / value / expression)