In PostgreSQL, factorial() is a mathematical function that returns the factorial of a given integer. We pass the integer (it accepts bigint), and it returns the factorial as a numeric value.

In mathematics, the factorial is the product of all positive integers less than or equal to a given positive integer. It’s denoted by that integer and an exclamation point.

Example

Here’s an example to demonstrate:

SELECT factorial(4);

Result:

24

Here’s how it arrives at that result:

4! = 4 × 3 × 2 × 1 = 24

So to get the factorial, we multiply all whole numbers from our chosen number down to 1.

As you can imagine, this has the potential to produce some large numbers. Here’s another example:

SELECT factorial(150);

Result:

57133839564458545904789328652610540031895535786011264182548375833179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000

Passing a Negative Value

Passing a negative value results in an error:

SELECT factorial(-4);

Result:

ERROR:  factorial of a negative number is undefined

However, in PostgreSQL 13 and earlier the function erroneously returns 1.

Passing a Null Value

Passing a null value results in null being returned:

SELECT factorial(null);

Result:

null

Passing the Wrong Argument Type

If the argument is not an integer, an error is returned:

SELECT factorial('cat');

Result:

ERROR:  invalid input syntax for type bigint: "cat"
LINE 1: SELECT factorial('cat');
                         ^

About Factorial

The Math is Fun website has a nice, simple explanation about how the factorial function works in mathematics, along with examples.