Factorial facts for kids

The factorial of a whole number n, written as n!,' is found by multiplying n by all the whole numbers less than it. For example, the factorial of 4 is 24, because 4 × 3 × 2 × 1 = 24. Hence one can write 4! = 24. For some technical reasons, 0! is equal to 1.

Factorial can be used to find out how many possible ways there are to arrange n objects.

For example, if there are 3 letters (A, B, and C), they can be arranged as ABC, ACB, BAC, BCA, CAB, and CBA. That would be 6 choices because A can be put in 3 different places, B has 2 choices left after A is placed, and C has only one choice left after A and B have been placed. In other words, 3×2×1 = 6 choices.

The factorial function is a good example of recursion (doing things over and over), as 3! can be written as 3×(2!), which can be written as 3×2×(1!) and finally as 3×2×1×(0!). N! can therefore also be defined as N×(N-1)!, with 0! = 1.

The factorial function grows very fast. There are 10! = 3,628,800 ways to arrange 10 items.

n! is not defined for negative numbers. However, the related gamma function is defined over the real and complex numbers (but the integers it is defined over are positive).

Related pages

• Exclamation mark
• Permutation

Images for kids

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  Amplitude and phase of factorial of complex argument