factorial
factorial — noun
1. A value that you calculate by taking a given whole number and multiplying it by
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.
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.
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.
The factorial of 10 is 3,628,800, a value that appears often in probability and statistics problems.
- 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 — adjective
1. Relating to the factors that affect or influence a result, especially in researc
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.
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.
factorial analysis: examining multiple contributing factors
The factorial structure of the survey results revealed several distinct factors that influenced student satisfaction.
Gabriel set up a factorial experiment to study how light and water together affect seed germination.
- 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
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!.
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!.
Before solving the probability problems, the students reviewed factorial notation and how it relates to permutations.
Putri wrote a factorial expression for the number of possible seating arrangements of six guests at a table.
文法句型
factorial + noun (notation / value / expression)