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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 `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;
}

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) {