Factorial

In Mathematics, factorial is a simple thing. Factorials are just products. An exclamation mark indicates the factorial. Factorial is a multiplication operation of natural numbers with all the natural numbers that are less than it. In this article, let’s discuss the factorial definition, formula and examples.

Definition

The multiplication of all positive integers say “n”, that will be smaller than or equivalent to n is known as the factorial. The factorial of a positive integer is represented by the symbol “n!”. The formula to find the factorial of a number is

n! = n × (n-1)×(n-2)×(n-3)× ….× 3×2×1

For an integer n≥ 1, the factorial representation in terms of pi product notation is

\(n! = \prod_{i=1}^{n}i\)

From the above formulas, the recurrence relation for the factorial of a number is defined as the product of factorial number and factorial of that number minus 1. It is given by

n! = n. (n-1) !

For example, the factorial of 10 is written as

10! = 10. 9 !

10! = 10 (9 ×8× 7× 6× 5× 4 ×3× 2 ×1)

10! = 10 (362,880)

10! = 3,628,800

Therefore, the value of 10 factorial is 3,628,800

The factorial operation is encountered in many areas of Mathematics such as algebra, permutation and combination, and mathematical analysis. Its primary use is to count “n” possible distinct objects.

Factorial Examples

Factorial of 5

We know that the factorial formula is

n! = n × (n-1)×(n-2)×(n-3)× ….× 3×2×1

So the factorial of 5 is

5! = 5× (5-1)× (5-2)× (5-3)× 1

5! = 5 ×4 ×3 ×2 ×1

5! = 120

Therefore, the factorial of 5 is 120

Factorial of 0

The factorial of 0 is 1

i.e., 0 ! = 1

According to the convention of empty product, the result of multiplying no factors is a nullary product. It means that the convention is equal to the multiplicative identity.

Factorials of Numbers 1 to 10

The list of factorial values from 1 to 10 are:

Factorial of a Number

Expansion

Value

1!

1

1

2!

2×1

2

3!

3 ×2× 1

6

4!

4 ×3× 2 ×1

24

5!

5× 4× 3× 2× 1

120

6!

6× 5 ×4 ×3× 2× 1

720

7!

7× 6× 5 ×4× 3× 2 ×1

5,040

8!

8× 7× 6× 5× 4× 3 ×2× 1

40,320

9!

9 ×8× 7× 6× 5× 4 ×3× 2 ×1

362,880

10!

10× 9×8× 7× 6× 5×4× 3× 2× 1

3,628,800

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