# Definition of factorial

We define the factorial of a number as the multiplication of all integers from that number to 1.

We use the symbol ! which is an exclamation mark to denote factorial and we put the exclamation mark next to a number.

For example,  5!  is read as five factorial and we can evaluate 5! by multiplying all integers from 5 to 1.

5!  = 5 × 4 × 3 × 2 × 1 = 20 × 6 = 120

## A more formal definition of factorial

Let n be a whole number, then n! read as n factorial represents the product of all whole number from n to 1

In other words, n! = n×(n - 1)×(n - 2)×(n - 3) ... 3×2×1

By definition 0! = 1 and 1! = 1

Evaluating factorials

1) Evaluate 6!

To evaluate 6!, find the product of all whole numbers from 6 to 1

6! =  6 × 5 × 4 × 3 × 2 × 1 = 20 × 6 = 720

Notice  that we have already computed 5! and 5! = 120. Therefore you could have just multiplied 120 by 6 to get 6 factorial.

6! = 6 × 5!

In general, n! = n × (n -1)!

Evaluate (8 - 3)!

(8 - 3)! = 5! = 120

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