## Calculate factorial

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 `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
```