What is the factorial of 0.5 (0.5!)?

If you use Excel and enter the following formula: =FACT(0.5) the answer will be one. However, if you open a more rustic tool such as the Windows Calculator and try again, you will get 0.886226925510.

So, how can a tool such as the Windows calculator come up with the correct answer when Excel can only return 1? What about the factorial of 0.75 (0.75!)? Again, Excel returns 1 whereas the Windows calculator gets the correct answer: 0.919062526898

Both numbers are close to one, but they are not exactly one.

The trouble is that Excel is using the general rule that states that the factorial is, in fact, the product of all integers in the series. So 4! Is given by =(4*3*2*1)=24. Unfortunately, the story does not end there for factorials.

When dealing with factorials the above works fine for integers. When dealing with non-integers (greater than zero), then we need the natural logarithm of the gamma function to get it to work. This function uses the concept of limits to determine the factorial of a number, so the factorial of 5 (5!) would be 119.99999998 when using gamma instead of the integer 120 (you can obviously round to 120, since it is effectively this number). For a discussion on the gamma function check this link:

http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html

Supposing the number you wish to find its factorial is located in cell A1, your formula using the gamma function would be:

=A1*EXP(GAMMALN(A1))

The last thing to remember is that this is for positive numbers only.

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