Factorial in PHP

Before we begin learning of Factorial in PHP, let us understand the term factorial. Factorial of a number is the product of all numbers starting from 1 up to the number itself. While calculating the product of all the numbers, the number is itself included.

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Factorial of a number is calculated for positive integers only. The factorial of 0 is always 1 and the factorial of a negative number does not exist. It is denoted by ‘!’ preceded by the number. Example n! where n is the number

So,

Factorial of 5! means factorial of 5

Factorial of 7! means factorial of 7

For example, the factorial of number 5 is:

5! =5*4*3*2*1 = 120

Similarly, the factorial of number 7 is:

7! = 7*6*5*4*3*2*1 = 5040

and so on..

Now how do we actually find the factorial, we can do it using

1. for loop (without recursion)
2. with recursion

Factorial Logic

The logic behind getting the factorial of the number is as per the following.

1. Get the number whose factorial is to be calculated.
2. Get all the numbers starting from 1 up to that number.
3. Get the multiplication of all the numbers.

Remember the factorial of 0! = 1.

How to Find Factorial in PHP?

We will learn further using different methods to calculate factorial of the given number using PHP code. Like using recursion, recursion with user input, without recursion, without recursion with user input.

About Recursion

Like other languages PHP also supports Recursion. What is recursion? When a function calls itself is termed as recursion. A recursive function calls itself within the function.

Example #1

In the following PHP program factorial of number 5 is calculated. This is a simple program using for loop. This for loop is iterated on the sequence of numbers starting from the number till 1 is reached.

Code:

<?php //example to calculate factorial of a number using simple for loop
//declaring the input number as 5
$input=5;
//declaring the fact variable as 1
$fact =1;
//iterating using for loop
for($i=$input; $i>=1;$i--) {
// multiply each number up to 5 by its previous consecutive number
$fact = $fact * $i;
}
// Print output of the program
echo '<br>'. 'The factorial of the number 5 is '. $fact
?>

Output:

Example #2

In the below program, we have used a simple HTML form with an input text and a submit button. The input box is used to get user input. The submit button is used to submit the form data. Followed by that is the PHP code to iterate for loop wherein all the logic is present, which we learned in the previous program. So now the same logic is used with an input form.

If the user inputs a positive number through the input box in the form, the factorial of that number is calculated and the result is printed.

Code:

<title> Factorial Program</title>

Enter a number

=1;$i--) { $fact = $fact * $i; } // Print output of the program echo '
'. 'The factorial of the number '.$input.' is ' . $fact; } ?>

Output :

Example #3

In the above two programs, we didn’t wrap the logic within a function. Here we have enclosed the main logic in a function and then called that function to calculate the factorial of the given number in PHP. Here the name of the function is Factorial_Function which finds the factorial of number 8.

Code:

//example to calculate factorial of a number using function
//defining the factorial function
function Factorial_Function($number) {
$input = $number;
$fact=1;
//iterating using for loop
for($i=$input; $i>=1;$i--) {
$fact = $fact * $i;
}
return $fact;
}
//calling the factorial function
$result = Factorial_Function(8);
echo 'Factorial of the number 8 is '.$result;
?>

Output :

Example #4

We know that recursion is calling a function within a function. In the following example, we will use recursion and find the factorial of the number using PHP code. The main logic is wrapped in a function name Factorial_Function. Within this function if the input is greater that one, then the same function is called again and if the input is less than or equal to 1 then one is returned.

Using Recursion

Code:

<?php //Example to demonstrate factorial of a number using recursion
//function containing logic of factorial
function Factorial_Function($input)
{
// if the input is less than or equal to 1 then return
if($input <=1) {
return 1;
}
// else do a recursive call and continue to find the factorial
return $input * Factorial_Function($input-1);  //doing a recursive call
}
echo "Factorial of 9 is ".Factorial_Function(9);
?>

Output :

Example #5

We have now learned about recursion. In the following program, we have used recursion, the recursion is applied to the number which is the input from the user in this example.

Code:

<title> Factorial Program</title>

Enter a number

'. 'The factorial of the number '.$input.' is ' . Factorial_Function($input); } ?>

Output:

Conclusion

This article has covered all the explanations and examples for finding the factorial of a number using PHP. Examples are explained using recursive and non-recursive ways, along with recursion explanation in context with the program. Hope this article was found informative to learn and grasp well.

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