Factorial Notation, Illustration, Rapid Questions, Examples, Important Topics For JEE Main 2024

Factorial Notation : Factorial is originated from the French word factorielle. At ancient time many countries made use of it in various calculations such as in Indian mathematics it was used between 300BCE to 400CE in Jain literature later in 6 ^th -century CE Jinabhadra described product rule of factorization, Bhaskara II used factorial in his work Lilavati. Arab Mathematician Alhazen formulate Wilson’s theorem having use of factorial with prime numbers.in 1677 British author Fabian Stedman made use of factorial in musical art known as change ringing.

Factorial Notation : As we have discussed continuous product of first n natural numbers is known as factorial value of n! is even except the case when n is 1, factorial is undefined for fractions or negative numbers, value of 0! is one as n! leads to consecutive product of positive integers   with difference of one so it will lead to 0 and multiplication of 0 with any value made the result as 0 which does not make sense in factorial hence value of 0! Is fixed as 1.

Factorial Notation Examples

Example 1: Find LCM of 7!, 3!, 5!?

Solution: Terms LCM is defined as least common product means a value which is first multiple of all the terms combined for example LCM of 4, 6 is 12 which is combinedly divisible by 4, 6.

Example 2: Find value of x if ?

Solution: Above equation could be written as

Example 3: Find value of x if ?

Solution: Using factorial expansion Above term could be written as

Example 4: Convert the given product in factorial form ?

Solution: Factorial is defined as continuous product of first n natural numbers could be written as

Example 5: Convert the given product in factorial form ?

Solution: Factorial is defined as continuous product of first n natural numbers is product of first odd natural numbers product of first even natural numbers could help here

Factorial Notation Rapid Question

Factorial Illustration

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Factorial Illustration And Examples

Factorial Illustration : Factorial is originated from the French word factorielle. At ancient time many countries made use of it in various calculations such as in Indian mathematics it was used between 300BCE to 400CE in Jain literature later in 6 ^th -century CE Jinabhadra described product rule of factorization, Bhaskara II used factorial in his work Lilavati. Arab Mathematician Alhazen formulate Wilson’s theorem having use of factorial with prime numbers.in 1677 British author Fabian Stedman made use of factorial in musical art known as change ringing .

Factorial Illustration Introduction

Factorial Illustration Introduction: As we have discussed continuous product of first n natural numbers is known as factorial, Factorial has some standard results which need to be remember.

1. Factorial does not follow distributive law when terms attached with addition, subtraction, multiplication and division symbols and
2. Product of n consecutive numbers is always divisible by n! for example has 4 terms than it must be divisible by
3. (1! +2! +3! +………. +n!) is perfect square only when n=1,3 this is because

Factorial Illustration Examples

Example 1: Find the value of (3+4)! And prove that it is not equal to ?

Solution: Value of Would be as 7! =

Example 2: Find the value of ( )! and prove that it is not equal to ?

Solution- Value of Would be as 6! =

Example 3: Find the value of ( )! And prove that it is not equal to ?

Solution: Value of ( )!  Would be as 3! =

Example 4. Convert the given product in factorial form ?

Solution: Factorial is defined as continuous product of first n natural numbers could be written as

Example 5: Convert the given product in factorial form ?

Solution: Factorial is defined as continuous product of first n natural numbers is product of first odd natural numbers product of first even natural numbers could help here

Factorial Illustration Rapid Question

Illustration:

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