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What is the Factorial function?

The factorial function is a mathematical formula represented by an exclamation mark "!". In the Factorial formula you must multiply all the integers and positives that exist between the number that appears in the formula and the number 1.

Here’s an example:

7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5.040

On this formula number 7 will be called 7th factorial and multiplied by all the numbers that appear on the example until number 1.

If at this stage you are about to give up I will confess that in your calculator appears a button that will calculates the factorial of the number that you want automatically. You should look for a button similar to "x!" Or "n!".

Examples of factorial formulas

1! = 1 * 1 = 1
3! = 1 * 2 * 3 = 6
10! = 1 * 2 * 3 … 8 * 9 * 10 = 3.628.800

What about the 0 factorial, how to calculate it? If we go back to the definition of factorial function we can see that it does not make sense to apply it in the case of "0". There are no positive numbers before 0 so 0 x 0 = 0.

However, it has been agreed that in the case of 0 factorial the result will be equal to 1:

0! = 0 x 0 = 1

The utility of the Factorial function

It is common to use Factorial functions to calculate combinations and permutations. Thanks to the Factorial you can also calculate probabilities.

For example:

If we have 4 colored pictures and want to hang them on the wall, one after another we can calculate the number of possible combinations:

4! = 1 * 2 * 3 * 4 = 24 possible combinations
factorial number function

Why are we called Factorial?

At this point you may be wondering why Factorial chose that name for its human resources software. Well, Factorial represents growth to the last power, a factorial growth of time, resources, productivity ... Factorial's human resources software allows the company to optimize its resources to keep growing factorially!