An online calculator to calculate the factorial of a positive integer.
If n is a positive integer, then the factorial of n written as \( n! \) (read as "n factorial") is given by
\( n ! = n \times (n-1) \times (n-2)....2 \times 1 \)
with \( 0! = 1\).
Example 1
\( 2! = 2 \times (2 - 1) = 2 \times 1 = 2 \)
\( 10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3628800 \)
The factorial of positive integers increases very quickly.
Example 2
\( 40! = 8.159152832478977\times 10^{47} \)
\( 100! = 9.33262154439441 \times 10^{157} \)
Note: the powers of 10 are written with an "E", see example below.
Factorials are used in the calculation of combinations. The combination of n objects taken r objects at a time is written as \( C(n,r) \) and is given in terms of factorials by the formula
\( C(n,r) = \dfrac{n!}{(n - r)! r!}\)
Factorials are used in the calculation of permutations. The permutation of n objects taken r objects at a time, where order is important, is written as \( P(n,r) \) and is given in terms of factorials by the formula
\( P(n,r) = \dfrac{n!}{(n - r)}\)
Factorials are used in series of functions in calculus and in turn these series are used in electronic calculators to compute functions such sin(x), cos(x), ln(x), ex. We list here some examples of functions given by series.
a) \( e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + ... \)
b) \( sin(x) = x - x^3/3! + x^5/5! + ... \)
c) \( cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ... \)
