Factorial
Content
- What is the factorial function?
- How to calculate the factorial function of a number?
- The zero factorial
- Applications of the factorial function
- Factorial of a large number
- Getting the factorial
- 6.1.- 2 factorial
- 6.2.- 3 factorial
- 6.3.- 4 factorial
- 6.4.- 5 factorial
- 6.5.- 6 factorial
- 6.6.- 7 factorial
- 6.7.- 8 factorial
- 6.8.- 9 factorial
- 6.9.- 10 factorial
- 6.10.- 11 factorial
- 6.11.- 12 factorial
What is the factorial function?
The factorial function is a mathematical formula represented by an exclamation point "!". Given a number n, "n factorial" (written n!). This exclamation means that all positive integers must be multiplied from the assigned number to the number one, in other words, it is the product of all positive integers less than or equal to "n".
How to calculate the factorial function of a number?
To calculate the factorial function of a number we must multiply a series of numbers that descend, or you can also interpret a series of numbers from the number 1 to the number from which you want to know the factorial.
You are asked to find the factorial of 4, you can also say “4 factorial”, the mathematical representation would be: 4!
4! = 1 x 2 x 3 x 4
It can also be represented on the contrary
4! = 4 x 3 x 2 x 1
As long as you understand every number between the one and the number from which you are asked to find the factorial function, the order of the products is not altered.
4! = 24
Note: It is recommended to accommodate the numbers from highest to lowest.
Examples:
3! = 3 x 2 x 1 = 6
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
2! = 2 x 1 = 2
Exercise:
The zero factorial
It is a curious fact and there are several mathematical checks of why the zero factor is 1 (0! = 1), in other words, the zero factor is a special case.
Suppose you want to order colored boxes, but you have 0 boxes to order, therefore there is only one way to combine since not being able to order something is considered as a possibility.
0! = 1
Applications of the factorial function
When calculating the factorial number of a number it allows to know combinations and permutations, by means of the combinations the probabilities can be calculated.
Suppose that 3 balls of different colors (red, blue and green) are contained in a box. How many are the combinations that exist when taking out the 3 balls?
3! = 6
There are 6 combinations:
- Red, blue and green.
- Red, green and blue.
- Blue, red and green.
- Blue, green and red.
- Green, red and blue
- Green, blue and red
Factorial of a large number
Since the factor values are increasing with respect to the increase in the number "n" it is convenient to use methods that allow obtaining an approximate number.
The Stirling formula provides a good estimate of the factorial of a number:
n! ≈ (2Π)^{1/2}e^{(-n)}n^{(n + 1/2)}
- e It is a mathematical constant with an approximate value of 2.71828.
Learn more about: “Euler number”. →
- Π It is a mathematical constant with an approximate value of 3.14159.
Learn more about: “Pi number”. →
Getting the factorial
You are going to obtain the factorial of different numbers using different procedures.
2 factorial
Procedure with exact result:
3 factorial
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4 factorial
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5 factorial
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6 factorial
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7 factorial
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8 factorial
Procedure with exact result:
9 factorial
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10 factorial
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11 factorial
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12 factorial
Procedure with exact result:
Content
- What is the factorial function?
- How to calculate the factorial function of a number?
- The zero factorial
- Applications of the factorial function
- Factorial of a large number
- Getting the factorial
- 6.1.- 2 factorial
- 6.2.- 3 factorial
- 6.3.- 4 factorial
- 6.4.- 5 factorial
- 6.5.- 6 factorial
- 6.6.- 7 factorial
- 6.7.- 8 factorial
- 6.8.- 9 factorial
- 6.9.- 10 factorial
- 6.10.- 11 factorial
- 6.11.- 12 factorial
Arithmetic Tutorials
- Arithmetic
- Number
- Natural
- Integer
- Rational
- Irrational
- Complex
- Even
- Odd
- Prime
- Decimal
- Ordinal
- Pi number
- Euler number
- Golden number
- Place value
- Sum
- Subtraction
- Multiplication
- Division
- Rule of signs
- Signs of greater and lesser
- Absolute value
- Fraction
- Multiples
- Least common multiple (lcdm)
- Divisor
- Greatest common divisor (gcd)
- Exponent
- Logarithm
- Root (square y cube)
- Factorial
- Percentage
- Rule of three