PHP program to print factorial of a number:
The below program prints factorial of a number using a loop. The PHP echo statement is used to output the result on the screen. The factorial of a number can be calculated for positive integers only and is represented by n!.
n! = n*[n-1]*[n-2]*......*1 0! = 1
Example
DOCTYPE html>
Output
10! = 3628800
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We already know how to get the factorial of a number in other languages. Let’s see how this is done in PHP using both recursive and non-recursive ways. Examples:
Input : 5 Output : 120 Input : 10 Output : 3628800
Method 1: Iterative way In this method, we simply used the for loop to iterate over the sequence of numbers to get the factorial.
PHP
Output:
3628800
Time Complexity: O[N] where N is the number of which factorial is being calculated
Auxiliary Space: O[1]
Method 2: Use of recursion In this method we are calling the same method to get the sequence of the factorial.
PHP
Output:
3628800
Time Complexity: O[N] where N is the number of which factorial is being calculated
Auxiliary Space: O[N]
Introduction to 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.
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
- for loop [without recursion]
- with recursion
Factorial Logic
The logic behind getting the factorial of the number is as per the following.
- Get the number whose factorial is to be calculated.
- Get all the numbers starting from 1 up to that number.
- 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:
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:
Factorial Program
Enter a number
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:
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:
Factorial Program
Enter a number
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.
Recommended Articles
This is a guide to Factorial in PHP. Here we discuss the basic concept and how to find the factorial of a number in PHP with different examples. You may also look at the following article to learn more –
- PHP Math Functions
- PHP String Functions
- PHP Constants
- Factorial in Java