Factorial Meaning: Definition, Examples, and Translations
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factorial
[fรฆkหtษหriษl ]
Definitions
mathematics
The product of an integer and all the integers below it; e.g., factorial four ( 4! ) is equal to 24 (4 ร 3 ร 2 ร 1).
Synonyms
factorialize.
Which Synonym Should You Choose?
| Word | Description / Examples |
|---|---|
| factorial |
As a noun, 'factorial' can also describe something related to a mathematical factorial in more general terms.
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| factorialize |
This verb means to compute the factorial of a number. This term is often used in programming and computer science contexts.
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Examples of usage
- The factorial function is commonly used in mathematics.
- To calculate the factorial of a number, you multiply that number by all the positive integers less than it.
computing
A recursive function or algorithm that calculates the product of all positive integers up to a given number.
Synonyms
factorialize.
Which Synonym Should You Choose?
| Word | Description / Examples |
|---|---|
| factorial |
Used in mathematics to describe the product of all positive integers up to a specified number.
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Examples of usage
- The factorial algorithm is often used in programming for various computations.
- In computer science, understanding how to implement the factorial function efficiently is important.
Translations
To see the translation, please select a language from the options available.
Interesting Facts
Mathematics
- Used in permutations and combinations, it helps in counting how many ways items can be arranged.
- The factorial of 0 is 1, which is unique in math, even though zero isn't a number you can multiply.
- Factorials grow really fast; for example, 10! equals 3,628,800!
Historical Origins
- The concept traces back to the 19th century, with the term 'factorial' coined by French mathematician Christian Kramp in 1808.
- Its notation 'n!' was introduced by the mathematician Karl Weierstrass and became standard in mathematical literature.
- The use of factorial in mathematics allowed for advancements in combinatorics, probability, and statistics.
Computer Science
- Factorials are commonly used in algorithms, particularly in calculating permutations and combinations for coding problems.
- Many programming languages provide built-in functions to calculate factorials efficiently due to their importance in coding challenges.
- Calculating large factorials can lead to very big numbers, so special handling is necessary in computing to avoid overflow.
Pop Culture
- Factorial concepts appear in games and puzzles, especially those involving strategy and optimization.
- In various educational instances, factorials are featured in movies and TV shows portraying mathematicians or scientific themes.
- References to factorials can be found in modern memes and jokes among mathematicians and students as a badge of math culture.
Psychology
- Understanding factorials can improve logical thinking and problem-solving skills, important traits in cognitive development.
- People often find comfort in structured, logical mathematical processes, which factorials exemplify.
- Mathematics, including factorials, is sometimes used in therapeutic settings to encourage focus and calming through number patterns.
Origin of 'factorial'
The term 'factorial' was introduced by Christian Kramp in 1808. The concept of factorial has been fundamental in mathematics and computing, providing a way to calculate permutations and combinations. It has applications in various fields such as probability, statistics, and number theory.
See also: factorable, factorizable, factorize, factors.