What is the Factorial of Hundred?

The factorial of hundred is equal to 9.332622e+157. In this article, we explain what the factorial of a hundred is and how to calculate the factorial of a hundred. We also provide you factorials of the first thirty numbers.

What is the Factorial of Hundred and how is it calculated?

A factorial is represented by an exclamation mark (!) inserted after the digit whose factorial is to be calculated. 

The Factorial of Hundred is calculated in the following way

100! = 100 X 99 X 98 X 97…3 X 2 X 1

After multiplying, we get

=93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

= 9.332622e+157

What is a Factorial?

A factorial is a number obtained by multiplying all the numbers from 1 to that number. For example,

4! = 4 X 3 X 2 X 1

Hence

4! = 24

Hence, if we generalize the formula

n! = n X (n-1) X (n-2) X (n-3) …… 3 X 2 X 1

Hence,

n! = n.(n-1).(n-2).(n-3)………………..3.2.1

The origins of factorial are attributed to ancient Indian Mathematics. However, much of the function regarding factorial was developed only in the 18th and 19th centuries AD.

Here are some important facts to know about factorial

• Factorial of all positive real numbers except 0 and 1 is are even number
• The Factorial of 0 is equal to 1
• The factorial of a positive real number cannot be negative
• Factorials of numbers are extensively used in Permutation Combinations and Probability.
• The factorial of a number is always equal to the number multiplied by the factorial of 1 less the number. It is demonstrated as follows

n! = n.(n-1).(n-2).(n-3)…………..3.2.1

n! = n.[(n-1).(n-2).(n-3)…………..3.2.1]

n! = n.(n-1)!

So, for example, the factorial of hundred is equal to a hundred times the factorial of 99

100! = 100 . 99!

Factorials of the first Thirty numbers

Here, we list down the factorials of the first thirty numbers

Number (n)	Factorial of the number (n!)
1	1
2	2
3	6
4	24
5	120
6	720
7	5040
8	40,320
9	362,880
10	3,628,800
11	39,916,800
12	479,001,600
13	6,227,020,800
14	8,717,8291,200
15	1,307,674,368,000
16	20,922,789,888,000
17	355,687,428,096,000
18	6,402,373,705,728,000
19	121,645,100,408,832,000
20	2,432,902,008,176,640,000
21	51,090,942,171,709,440,000
22	1,124,000,727,777,607,680,000
23	25,852,016,738,884,976,640,000
24	620,448,401,733,239,439,360,000
25	15,511,210,043,330,985,984,000,000
26	403,291,461,126,605,635,584,000,000
27	10,888,869,450,418,352,160,768,000,000
28	304,888,344,611,713,860,501,504,000,000
29	8,841,761,993,739,701,954,543,616,000,000
30	265,252,859,812,191,058,636,308,480,000,000

Frequently Asked Questions (FAQs) about factorial of hundred

Question 1) What is a factorial of a hundred?

Answer) The factorial of hundred is 9.332622e+157

Question 2) Where are factorials used?

Answer) Factorials of numbers are used in Permutation and Combinations, and Probability.

Question 3) How is the factorial of 0 calculated?

Answer) The factorial of zero is calculated in the following way:

n! = (n+1)! / (n+1)

0! = 1! / 1

Hence

0! = 1 / 1

 = 1

Other Types of Factorials

Double Factorial

Double Factorial of a number, denoted by n!! Is the product of the numbers between 1 and n that have the same parity. That means that if n is odd, the double factorial of n is the multiplication of all odd numbers between 1 and n. Similarly, if n is an even number, the double factorial of n is equal to the multiplication of all even numbers between 1 and n. It is illustrated below:

When n is an odd number

n!! = n × (n-2) × (n-4) × (n-6) × ….. × 1

When n is an even number

n!! = n × (n-2) × (n-4) × (n-6) × …..× 2

Primorial

Primorial is a type of factorial that, instead of natural numbers, is a product of prime numbers. It is denoted by a ‘#’. Thus, the primorial for the nth prime number is the multiplication of all prime numbers up to n. For instance, to evaluate the primorial of the 7th prime number, i.e 17, we do the following:

p_n# = p₁₇# = 2 × 3 × 5 × 7 × 11 × 13 × 17 = 510,510

Hyperfactorial

Hyperfactorial is a type of factorial that is calculated by multiplying the natural number powered by the number itself until n to the power n. It is denoted by H and is shown below

H(n) = 1¹ × 2² × 3³ × 4⁴ × 5⁵ × …….. × (n-1)^(n-1) × nⁿ

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That’s It

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