Factorial - Recursive Formula

The recursive formula is $n! = n \times (n-1)!$ This says: to compute $n!$, multiply $n$ by the factorial of $n-1$. For example, $5! = 5 \times 4!$, and $4! = 4 \times 3!$, and so on, until you hit the base case.

Notice how each step reduces the problem size by $1$. You're breaking a big problem into a smaller one, trusting that the recursive call will handle it. That trust feels strange at first. "How can I use the answer before I have it?" But you're not. You're defining a relationship between answers. The math guarantees it works.