# Factorial

From Number

## Definition

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

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

## Behavior

### Initial values

The initial values of for are given as: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, [SHOW MORE] 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 . - Maximum product over additive partitions
- Landau's function is the maximum lcm over additive partitions.
- Primorial is the product of the first few primes.