There is no short cut for this.

In GMAT particularly you dont need to concentrate on calculations.

Just remember calculations till 6! which is easy enough with practice.
2!=2
3!=6
4!=24
5!=120
6!=720
7!=5040
8!=40320
9!=362880
10!=3628800

I could do all this in less than 10 secs because i knew all the calculations till 6!.

Hope this helps

Ian hit it on the head. (I really like coming after this guy because he's spot on.)

The GMAT will require factorials in the context of Combination and Permutation problems. The way those formulas are set up to divide factorials before you actually calculate them.

For example:

8_C_3 = 8!/ [3!(8-3)!] = 8*7*6*5*4*3*2*1 / 3*2*1 * 5*4*3*2*1

Here the 5 through 1 factors in the numerator and denominator cancel to 1 leaving:

8*7*6 / 3*2*1

and the 3*2 in the denominator cancel the 6 factor in the numerator. That leaves simply 8*7, or 56.

I have lots of students who want to calculate 8! then divide it by 5! and 3! but canceling common factors in the numerator and denominator is WAY faster and less prone to error.

This is the manner in which factorials are tested on the GMAT.