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:
pn# = 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
That’s It
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