Factorial

Definition

Let $n$ be a nonnegative integer. The factorial of $n$, denoted $n!$, and read as n factorial, is defined as the product of all the natural numbers from $1$ to $n$. Note that $0!$ is defined as $1$.

$n!$ is also the order of the symmetric group, or the group of all permutations, on a set of size $n$.

Behavior

Initial values

The initial values of $k!$ for $k=0,1,2,3,4,\dots$ are given as:

1, 2, 6, 24, 120, 720, 5040, 40320, 362880 View list on OEIS

Related notions

• lcm of all numbers so far: This is the exponential of the second Chebyshev function and also equals the exponent of the symmetric group of degree $n$.
• Maximum product over additive partitions
• Maximum lcm over additive partitions
• Primorial is the product of the first few primes.