The FACT function calculates the factorial of a number n where n is traditionally a positive integer. The factorial of n is defined as:
n * (n-1) * (n-2) *…….* 4 * 3 * 2 * 1
with the factorial of n = 0 being defined as 1.
For example:
FACT(4)
returns 24 as calculated by 4 * 3 * 2 * 1.
FACT can be used to determine the probability of ordered events. For example, the probability of drawing 6 balls, numbered 1 through 6, in the precise sequence 1, 2, 3, 4, 5, 6 is given by the formula:
1/FACT(6)
which returns 0.001389.
FACT can be used with numbers having a fractional part. The factorial of x where x is not an integer, is calculated using the formula:
x * (x - 1) * (x - 2) *…..* (x - n)
where 2 > (x - n) > 1.
The factorial of any number 0 < x < 1 is defined as 1. For example:
FACT(0.5) returns 1
FACT(1.5) returns 1.5
FACT(3.5) returns 3.5 * 2.5 * 1.5 = 13.125
Factorial functions do not work with negative numbers, so if you enter a negative number Ability displays #VALUE in the cell.
Factorial calculations can create very large numbers. The factorial of any number bigger than 170 will cause overflow errors and #VALUE will be returned.
See also: