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!

Abraham de Moivre was the person who first introduced Stirling's formula.  His friend James Stirling is the one who found that the constant is $\sqrt{2\pi}$; de Moivre only knew it numerically.
Demoivre used it to approximate the probability that the number of heads you get when you toss a coin 1800 times is $x$, for $x$ not too many standard deviations away from 900.  He wrote about this in his book titled The Doctrine of Chances (google the title!).  The title of the book is in effect 18th-century English for "the theory of probability".  The phrase appears again in Thomas Bayes' famous posthumous paper "An essay towards solving a problem in the doctrine of chances" (google that title too).  De Moivre derived the bell-shaped curve
$$
x\mapsto \text{constant} \cdot e^{-x^2/2}
$$
from this formula.
