Introduction to Factorial notation

Factorial of 2 is 1 x 2 = 2

Factorial of 3 is 1 x 2 x 3 = 6

Factorial of 4 is 1 x 2 x 3 x 4 = 24, and so on

Factorial of a number 'n' is the product of the first 'n' natural numbers. Alternatively, this definition can be written as: Factorial of a number is the product of all numbers from 1 to that number.

Consider 'n' as any natural number, then, the first 'n' natural numbers are the natural numbers from 1 to the  number 'n'.The product of the first 'n' natural numbers is the product of every number from 1 to the number 'n'. The factorial of n is the product of every number from1 to 'n'.

Consider the natural number '4'. Its factorial is equal to the product of each number from 1 to 4. Thus

Factorial of 4	= 1 x 2 x 3 x 4
	= 24

Important points

• The symbol for factorials is exclamation mark "!". For example, factorial of 4 is represented by 4!
• Factorials are not defined for negative numbers, decimals, fractions, and irrational numbers.
• Factorials are only defined for natural numbers, that is, whole numbers from 1 to any number.
• Factorial of 0 is 1
• Factorial of 1 is 1

Books recommended for learning:

• Factorials from 1 to 100,000
• 505 Factorial Notation & Linear Permutations
• Pattern Numbers
• A Calculus for Factorial Arrangements

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