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Calculate factorial

importance: 4

The factorial of a natural number is a number multiplied by "number minus one", then by "number minus two", and so on till 1. The factorial of n is denoted as n!

We can write a definition of factorial like this:

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

Values of factorials for different n:

1! = 1
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
5! = 5 * 4 * 3 * 2 * 1 = 120

The task is to write a function factorial(n) that calculates n! using recursive calls.

alert( factorial(5) ); // 120

P.S. Hint: n! can be written as n * (n-1)! For instance: 3! = 3*2! = 3*2*1! = 6

By definition, a factorial is n! can be written as n * (n-1)!.

In other words, the result of factorial(n) can be calculated as n multiplied by the result of factorial(n-1). And the call for n-1 can recursively descend lower, and lower, till 1.

function factorial(n) {
  return (n != 1) ? n * factorial(n - 1) : 1;
}

alert( factorial(5) ); // 120

The basis of recursion is the value 1. We can also make 0 the basis here, doesn’t matter much, but gives one more recursive step:

function factorial(n) {
  return n ? n * factorial(n - 1) : 1;
}

alert( factorial(5) ); // 120