September 14, 2024

What is the factorial of 100

What is the factorial of 100 ?

What is Factorial?

The factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n.

For n>0, n! = 1×2×3×4×…×n

For n=0, 0! = 1

Factorial definition formula (In product notation)   $n!&space;=&space;\left\{\begin{matrix}&space;1,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;n=0\\&space;\prod_{k=1}^{n}&space;,&space;n>0&space;\end{matrix}\right.$

Examples:

1! = 1

2! = 1×2 = 2

3! = 1×2×3 = 6

4! = 1×2×3×4 = 24

5! = 1×2×3×4×5 = 120

What is the factorial of 100 ? (How to calculate factorial of 100 )

We know that if n be a number, then its factorial is given by

n! = n × (n – 1) × (n – 2) × (n – 3) × … … × 1

Here our given number is 100. Thus taking n = 100, we get

100! = 100 × (100 – 1) × (100 – 2) × (100 – 3) × … … × 1

= 100 × 99 × 98 × 97 × … … × 1

= 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

In scientific notation this is equivalent to $9.3326215443944152681699238856267\times$ $10^{157}$

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( FAQs)

1. What is the factorial of 100?

Ans. The factorial of 100 is exactly equal to  93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

The approximate value of 100! is 9.3326215443944E+157.

2. How many zeros at the end of 100 factorial?

Solution : There are 24 zeros at the end of 100 factorial .

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