PHP | Factorial of a number

In mathematics, the factorial of a number is the product of all positive integers less than or equal to that number. It is denoted by n!. The factorial of a number can be expressed mathematically as:

 n! = n * (n-1) * (n-2) * ........ * 1

Methods to Calculate Factorials in PHP

There are several methods to calculate the factorial of a number in PHP. Let’s explore some of the most common approaches.

1. Using a Loop

One of the most straightforward ways to calculate the factorial of a number is by using a loop. We will multiply all integers from 1 to the given number. 

Now, let us understand with the help of the example:

<?php
function factorial($n) {
    $result = 1;
    for ($i = 1; $i <= $n; $i++) {
        $result *= $i;
    }
    return $result;
}

echo "Factorial of 5 is " . factorial(5);  // Output: Factorial of 5 is 120
?>

Factorial of 5 is 120

In this example:

• We define a function factorial($n) that calculates the factorial of the number.
• The loop runs from 1 to $n, multiplying each number with $result to accumulate the product.
• Finally, the result is returned.

2. Using Recursion

Recursion is another elegant way to calculate the factorial of a number. In this method, the function calls itself, reducing the number until it reaches the base case (0! = 1).

Now, let us understand with the help of the example:

<?php
function factorial($n) {
    if ($n == 0) {
        return 1;
    }
    return $n * factorial($n - 1);
}

echo "Factorial of 5 is " . factorial(5);  // Output: Factorial of 5 is 120
?>

Factorial of 5 is 120

In this example:

• The base case for recursion is when $n is 0. In that case, the factorial is 1.
• The recursive case multiplies $n by the factorial of n-1.
• The function keeps calling itself until the base case is reached.

3. Using PHP’s Built-In gmp_fact() Function

If you need to calculate the factorial of very large numbers, PHP provides the gmp_fact() function in the GMP (GNU Multiple Precision) library, which handles large integers more efficiently.

Now, let us understand with the help of the example:

<?php
$factorial = gmp_fact(5);
echo "Factorial of 5 is " . gmp_strval($factorial);  // Output: Factorial of 5 is 120
?>

In this example:

• The gmp_fact() function calculates the factorial of the number, and gmp_strval() converts the result into a string for easy display.
• This method is highly efficient for very large numbers because it supports arbitrary-precision arithmetic.

4. Using bcMath Functions for Large Numbers

For extremely large numbers, PHP's bcMath library can be used to handle arbitrary-precision numbers. The bcMul() function can be used to calculate the factorial by multiplying the numbers.

Now, let us understand with the help of the example:

<?php
function factorial($n) {
    $result = '1';  // bcMath functions work with strings
    for ($i = 2; $i <= $n; $i++) {
        $result = bcmul($result, (string)$i);  // Multiply result by i
    }
    return $result;
}

echo "Factorial of 5 is " . factorial(5);  // Output: Factorial of 5 is 120
?>

In this example:

• The bcmul() function multiplies two numbers (in string format) and returns the result as a string, which helps to avoid overflow issues when dealing with large integers.
• This approach is helpful when dealing with very large numbers that exceed PHP’s default integer size.

Conclusion

In this article, we explored different methods to calculate the factorial of a number in PHP. Whether you choose to use a loop, recursion, built-in functions like gmp_fact(), or even libraries like bcMath, the choice depends on the size of the numbers and the requirements of your application.