# 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

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000142

### Initial values

Here are the values of for small : .

## 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
- Maximum lcm over additive partitions
- Primorial is the product of the first few primes.