What is the purpose of Stirling's approximation to a factorial? Stirling approximation to a factorial is
$$
    n! \sim \sqrt{2 \pi n} \left(\frac{n}{e}\right)^n. 
$$
I wonder what benefit can be got from it?
From computational perspective (I admit I don't know too much about how each arithmetic operation is implemented and which is cheaper than which), a factorial $n!$ contains $n-1$ multiplications.
In Stirling's approximation, one also has to compute one division and $n$ multiplications for $\left(\frac{n}{e}\right)^n$, no? Plus two multiplication and one square root for $\sqrt{2 \pi n}$, how does the approximation reduce computation?
There may be considerations from other perspectives. I also would like to know. Please point out your perspective if you can.
Added: For purpose of simplifying analysis by Stirling's approximation, for example, the reply by user1729, my concern is that it is an approximation after all, and even if the approximating expression converges, don't we need to show that the original expression also converges and converges to the same thing as its approximation converges to? 
Thanks and regards!

Stirling's approximation is used extensively in Physics, in Boltzmann's description of entropy:
$$ S = k \log_e W$$
Where W is the number of possible permutations of a group of materials, given by
$$W = \frac{N!}{\prod_i N_i!}$$
Taking the the approximation makes the maths much easier.
