Numbers: glossary

Factorials

When mathematicians write 5! the exclamation mark does not express surprise or excitement. It is just a convenient way of writing 'factorial 5'. This means the number you get by multiplying together -
1 x 2 x 3 x 4 x 5
- which comes to 120.

Factorials of other numbers are calculated in the same way. Factorial 10 or 10! is -
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10
- which comes to quite a large number, 3,628,800.

Factorials are useful in working out the number of different ways you can arrange things. Factorial n is the number of ways n things can be arranged in a line. So if you had five garden gnomes in your front garden, they could be lined up in 5! or 120 different ways.

In the same way, eleven in a football team can stand in a row in 11! ways and a deck of 52 playing cards can be ordered in 52! different ways which is a huge number with 68 digits.

Here are the first ten factorials -
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5,040
8! = 40,320
9! = 362,880
10! = 3,628,800

Based on the book Numbers: Facts, Figures & Fiction.

Updated 1 June 2003.