factorials... I have no idea why this code works

Question

I came across an exercise on freecodecamp that required writing a code that would return the factorial for a given integer and gave this example: For example: 5! = 1 * 2 * 3 * 4 * 5 = 120f.

I get how the math works but I couldn't really wrap my head around how to code it until I found something here, n stackoverflow, but without an explination of why it works, that resembled this:

function factorialize(num) {
  if(num === 0) {
    return 1;
  } else {
    return num * factorialize(num - 1);
  }
}

factorialize(5);

I don't really understand how this is iterating through all the integers that are less than or equal to num. Can anybody help explain this to me?

Answer 1

It's a recursive function.

Calling factorialize with 5 does the following:

Is 5 equal to 0? No, so then:

return num * factorialize(num - 1); 

Substituting 5 for num means it is actually returning:

5 * factorialize(5-1)

So we can simplify that to

5 * (factorialize(4))

Which then must call factorialize on the second half of the statement to computer the return value.

So you can imagine, factorialize is called again with num = 4. Since num is not equal to zero, it also returns the same num * factorialize(num-1). The original statement is now:

5 * (4 * factorialize(3))

and so it must call itself again... and again... until we have

5 * 4 * 3 * 2 * 1 * factorialize(0)

which then actually returns a single number - this is called a base case so it doesn't infinitely recurse on itself. It returns 1.

Resulting in

5 * 4 * 3 * 2 * 1 * 1

I would argue the base case should be if (num == 1). Either way it works

Edit based on comment: The 0 makes sense, it obviously now covers 0 factorial. Thanks! With the base case of num == 1 it would only work for factorialize with a parameter num > 0.