Factorial Symbol

! Factorial, in Mathematics, is a very essential function, which is defined as the product of all positive integers, which are less than or equal to a given integer. It is denoted by that positive integer number, followed by an exclamation mark (!). It also means, multiplication of numbers starting from the given number till 1.

It can also be said as a function, which multiplies the given number, with every natural number below it. For example, factorial of 5 is represented as 5!.

History of factorial

During the period 1677, a British author named Fabian Stedman, defined factorial, equivalent to change ringing. The term change ringing was used in the musical performance, where the musicians would ring various tuned bells. And finally in the year 1808, Christian Kramp, a mathematician from France, introduced the symbol of factorial which is !.

Factorial symbol calculator

Eg, What is a factorial of 6? Enter 6 into the input box and click Calculate button.

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The formula for factorial is:

n! = n × (n – 1) × (n – 2) × …. × 1

n denotes any positive integer number.

For example, let’s see how to calculate the factorial of 5 (5!)

5! = 5 × 4 × 3 × 2 × 1 = 120

Example: In how many different ways the letters can be arranged without repeating?

For 1 letter, i.e., a there is only 1 way: a

For 2 letters, i.e., ab there are 1 × 2 = 2 ways: ab, bas

For 3 letters, i.e., abc there are 1 × 2 × 3 = 6 ways: abc, bca, cba, bac, cab, acb

For 4 letters, i.e., abcd there are 1 × 2 × 3 × 4 = 24 ways

And so on….

The formula is n!.

In how many different ways the 0 letters can be arranged? The answer is simple, just 1.

How to use the factorial symbol?

Factorials are mainly used in the calculation of Permutations and Combinations and its corresponding coefficient, in terms of binomial expansions. They have been generalised to include non-integral numbers.

Example 1: In how many different ways can 5 people stand 1st, 2nd or 3rd position?

There are many possibilities. Let’s assume 5 people are named as a, b, c, d, e. Then the combination would be like abc, bca, cab, cba, acb and so on…

However, there is a formula to calculate the possibility.

5!(5 – 3)! = 5!2! = 5 × 4 × 3 × 2 × 12 × 1

Cancelling 2 × 1, the answer would be 5 × 4 × 3 = 60

Therefore, there are 60 ways 5 people can stand 1st, 2nd or 3rd position.

Example 2: In how many different ways the word ‘little’ can be arranged?

The given word has 6 words. The given word has 2 letters (l, t) which are repeating. Hence the formula to calculate the possibility is

6!(2! × 2!)

= 6 × 5 × 4 × 3 × 2 × 1(2 × 1) × (2 × 1)

= 6 × 5 × 4 × 32 × 1

= 180

Therefore, the given word can be re-arranged 180 times.

Interesting facts about factorials

Listed below are few facts about factorials:

There is an interesting fact about 0. The factorial of 0 is 1. i.e., 0! = 1. The factorial is mostly used in permutation and combination. When there are 0 objects, there is exactly one way to arrange zero objects. This statement means there is only 1 permutation for zero objects, namely the empty set Ø.
There cannot be a factorial for negative integer numbers, since negative integer numbers are undefined.
The factorial in Wolfram language is represented as factorial [n] or n!.
Factorial of half (12) is half of square root of pi (π). (12)! = √π

How to type factorial symbol on PC Windows, Mac, phone, word, excel and powerpoint

Nowadays, calculations can be performed in almost all devices for ease.

On PC Windows
Factorial symbol (!) can be typed by pressing the keys shift + 1 (below the function keys towards the top of the keyboard) together.
On Macbook
The factorial symbol (!) can be typed by holding the keys Shift + letter E together.
On Android Phone
the factorial symbol (!) can be typed by navigating to the numeric keyboard by pressing ?123 key. Then the ! can be found.
In Microsoft Word, Excel And Powerpoint
- Open the document you want to insert.
- Place the cursor where the symbol is needed.
- Click on Insert tab from the top menu.
- Click on Symbol option.
- Select Basic Latin for the field ‘subset’.
- Select ! symbol and click on Insert.
- Click on Close button.
- Click on Insert button.

Codes of factorial symbol

It is very essential to know the codes of all mathematical symbols.

Following are the various codes of factorial symbol:

Unicode

U+0021

Alt Code

Alt 33

ASCII Code

33

Hex Code

& #x21;

HTML Code

& #33;

CSS Code

\0021

HTML Entity

& excl;

Frequently Asked Questions

Listed below are few questions which mostly comes in mind about factorial:

1. How is factorial calculated?
Factorial is usually calculated by multiplying a number, with every number below it. For example, 6! = 6 × 5 × 4 × 3 × 2 ×1 = 720
2. Can negative numbers have a factorial?
No, negative numbers cannot have factorials.
3. For which number, the largest factorial is calculated?
The number 170. This number has the largest factorial.
4. Does 0 have a factorial?
Yes. 0! = 1.
5. In what way the factorials are used?

The factorial of a number is the product of that number, till it goes down to 1 and not vice versa.

Another usage of factorial is it is used in permutation and combinations. It is actually to count in how many different ways, we can choose things from a grouping of things.
6. Can there be infinity factorial?
Since infinity is undefined and it cannot be reached, unlike natural numbers, it is not possible to have a factorial.
7. Can there be factorial for decimal numbers?
Yes, there can be factorial for decimal numbers. But factorials of decimal numbers are called as Gamma Function.

Conclusion

This article has explained about the concept of factorial in a precise manner, with examples. Hope the reader finds it interesting to read.

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