Factorial: meaning, definitions and examples
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factorial
[fækˈtɔːriəl ]
Definitions
mathematics
The product of an integer and all the integers below it; e.g., factorial four ( 4! ) is equal to 24 (4 × 3 × 2 × 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.
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.
Translations
Translations of the word "factorial" in other languages:
🇵🇹 fatorial
🇮🇳 फैक्टोरियल
🇩🇪 Fakultät
🇮🇩 faktorial
🇺🇦 факторіал
🇵🇱 silnia
🇯🇵 階乗 (kaijō)
🇫🇷 factorielle
🇪🇸 factorial
🇹🇷 faktöriyel
🇰🇷 팩토리얼 (paektorial)
🇸🇦 عاملي
🇨🇿 faktoriál
🇸🇰 faktoriál
🇨🇳 阶乘 (jiē chéng)
🇸🇮 faktorial
🇮🇸 stuðull
🇰🇿 факториал
🇬🇪 ფაქტორიალი
🇦🇿 faktorial
🇲🇽 factorial