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Factorial Calculator

Calculate Factorial of a number. Learn more about 0 factorial, 100 factorial, negative factorial and formula for calculating n factorial

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Factorial


Find the factorial of the given number

Factorial of 100 is 9.332621544394418e+157

What is factorial?

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  • Meaning of Factorial:

    Factorial of a number is the result we get on multiplication of the given number by all numbers below it upto 1. It is only applicable to integers > 0. For eg. Factorial of 3 is equal to 3 x 2 x 1 = 6

    Notation: Factorial of a number is denoted by the exclamation symbol followed by the number.(x!) or Fact(x).

  • Factorial Formula .

    (factorial of n) n! =n x (n-1) x (n-2) x ....1 = n x (n-1)!

  • Factorial example.

    1! = 1
    2! = 2x1 = 2
    3! = 3x2x1 = 6
    4! = 4x3x2x1 = 24
    5! = 5x4x3x2x1 = 120

Simplifying factorials / Calculating factorials

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  • n Factorial Formula

    As we know that we have a formula for finding the factorial of the given number.So lets see how to implement the formula and get the result.

    It is n x (n-1) x (n-2) x ....x 1

    Factorial of 5
    According to our formula n =5. 5! = 5 x (5-1) x (5-2) x (5-3) x..1
    5! = 5 x 4 x 3 x 2 x 1
    5! = 120

0 Factorial / Zero Factorial

  • Factorial of 0 is 1.

    Lets discuss how 0! is 1.

    We know that n! = n x (n-1)! ==> n = n!/(n-1)! this means the following,

    (n-1)! = n!/n

    if n = 1

    it becomes 0! = 1!/1 = 1

    From the above we conclude that Zero Factorial is 1

Is there a Negative Factorial

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  • No, there is no negative factorial.

  • Factorials are defined only for non-negative integers. For example, the factorial of 4 is 24, the factorial of 0 is 1, and the factorial of -1 is undefined.

  • One reason for this is that factorials are used to count the number of ways to arrange or select objects. For example, there are 6! ways to arrange 6 different objects in a row. However, there is no such thing as a negative number of objects, so it does not make sense to define a factorial for a negative number.

  • Another reason for not defining negative factorials is that it would lead to mathematical contradictions.

Interesting Facts About Factorials

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  • Factorials can be used to calculate the number of ways to arrange a set of objects in a particular order. For example, there are 6! ways to arrange 6 different objects in a row.

  • Factorials can also be used to calculate the number of possible combinations of objects from a set. For example, there are 15 ways to choose 3 objects from a set of 5 objects.

  • Factorials grow very quickly, even for relatively small numbers. For example, 10! is over 3.5 million.

  • The largest factorial that can be calculated on a standard computer is 170!.

  • Factorials are related to the Fibonacci sequence. The Fibonacci sequence is a series of numbers where each number is the sum of the two previous numbers. The first few numbers in the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

  • Factorials can also be used to calculate the volume of a sphere.

  • Factorials are used in some encryption algorithms.

  • The factorial of a prime number is always greater than the prime number itself.

  • The sum of the reciprocals of the factorials is equal to the natural logarithm of e, Euler's constant.

  • The factorial of a number is equal to the product of all the positive integers less than or equal to that number.

Where are Factorials Used

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Factorials are used in many different areas of mathematics, including probability, statistics, combinatorics, and number theory. They are also used in many practical applications, such as:
  • Probability: Factorials can be used to calculate the probability of certain events happening. For example, the probability of getting 3 heads in a row when flipping a coin is 1/8, which can be calculated using factorials.

  • Statistics: Factorials are used in many statistical tests, such as the chi-squared test and the t-test. These tests are used to test the significance of differences between groups or to predict future outcomes.

  • Combinatorics: Factorials are used in combinatorics to count the number of ways to arrange or select objects. For example, the number of ways to arrange 6 different books on a shelf is 6!.

  • Number theory: Factorials are used in number theory to study the properties of prime numbers and other types of numbers.

Here are some specific examples of how factorials are used in the real world:
  • Computer science: Factorials are used in many computer science algorithms, such as the quicksort algorithm and the factorial algorithm.

  • Finance: Factorials are used in finance to calculate the price of options and other financial products.

  • Genetics: Factorials are used in genetics to calculate the probability of inheriting certain traits.

  • Manufacturing: Factorials are used in manufacturing to calculate the number of ways to assemble products.

  • Logistics: Factorials are used in logistics to calculate the number of ways to route vehicles and deliver goods.

Note: The content has inputs from Bard, the AI model from Google

Table of Factorial Numbers

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Factorial of Factorial Value

Factorial of 1

1

Factorial of 2

2

Factorial of 3

6

Factorial of 4

8

Factorial of 5

120

Factorial of 6

720

Factorial of 7

5040

Factorial of 8

40320

Factorial of 9

362880

Factorial of 10

3628800

Factorial of 11

3.99168 E+7

Factorial of 12

4.790016 E+8

Factorial of 13

6.2270208 E+9

Factorial of 14

8.71782912 E+10

Factorial of 15

1.307674368 E+12

Factorial of 16

2.092278988 E+13

Factorial of 17

3.55687428 E+14

Factorial of 18

6.402373705 E+15

Factorial of 19

1.216451004 E+17

Factorial of 20

2.432902008 E+18

Factorial of 21

5.109094217 E+19

Factorial of 22

1.124000727 E+21

Factorial of 23

2.585201673 E+22

Factorial of 24

6.204484017 E+23

Factorial of 25

1.551121004 E+25

Factorial of 26

4.032914611 E+26

Factorial of 27

1.088886945 E+28

Factorial of 28

3.048883446 E+29

Factorial of 29

8.841761993 E+30

Factorial of 30

2.652528598 E+32

Factorial of 31

8.222838654 E+33

Factorial of 32

2.631308369 E+35

Factorial of 33

8.683317618 E+36

Factorial of 34

2.95232799 E+38

Factorial of 35

1.033314796 E+40

Factorial of 36

3.719933267 E+41

Factorial of 37

1.376375309 E+43

Factorial of 38

5.230226174 E+44

Factorial of 39

2.039788208 E+46

Factorial of 40

8.159152832 E+47

Factorial of 41

3.345252661 E+49

Factorial of 42

1.405006117 E+51

Factorial of 43

6.041526306 E+52

Factorial of 44

2.658271574 E+54

Factorial of 45

1.196222208 E+56

Factorial of 46

5.502622159 E+57

Factorial of 47

2.586232415 E+59

Factorial of 48

1.241391559 E+61

Factorial of 49

6.08281864 E+62

Factorial of 50

3.04140932 E+64

Factorial of 51

1.551118753 E+66

Factorial of 52

8.065817517 E+67

Factorial of 53

4.274883284 E+69

Factorial of 54

2.308436973 E+71

Factorial of 55

1.269640335 E+73

Factorial of 56

7.109985878 E+74

Factorial of 57

4.05269195 E+76

Factorial of 58

2.350561331 E+78

Factorial of 59

1.386831185 E+80

Factorial of 60

8.320987112 E+81

Factorial of 61

5.075802138 E+83

Factorial of 62

3.146997326 E+85

Factorial of 63

1.982608315 E+87

Factorial of 64

1.268869321 E+89

Factorial of 65

8.247650592 E+90

Factorial of 66

5.44344939 E+92

Factorial of 67

3.647111091 E+94

Factorial of 68

2.480035542 E+96

Factorial of 69

1.711224524 E+98

Factorial of 70

1.197857166 E+100

Factorial of 71

8.504785885 E+101

Factorial of 72

6.123445837 E+103

Factorial of 73

4.470115461 E+105

Factorial of 74

3.307885441 E+107

Factorial of 75

2.480914081 E+109

Factorial of 76

1.885494701 E+111

Factorial of 77

1.45183092 E+113

Factorial of 78

1.132428117 E+115

Factorial of 79

8.94618213 E+116

Factorial of 80

7.156945704 E+118

Factorial of 81

5.79712602 E+120

Factorial of 82

4.753643337 E+122

Factorial of 83

3.945523969 E+124

Factorial of 84

3.314240134 E+126

Factorial of 85

2.817104114 E+128

Factorial of 86

2.422709538 E+130

Factorial of 87

2.107757298 E+132

Factorial of 88

1.854826422 E+134

Factorial of 89

1.650795516 E+136

Factorial of 90

1.485715964 E+138

Factorial of 99

9.332621544 E+155

Factorial of 100

9.332621544 E+157

Factorial of 120

6.689502913 E+198

Factorial of 150

5.713383956 E+262

Factorial of 175

1.124449491 E+318

Factorial of 200

7.886578673 E+374

Factorial of 300

3.060575122 E+614

Factorial of 365

2.510412867 E+778

Factorial of 500

1.220136825 E+1134

Factorial of 1000

4.0238726 E+2567

Factorial of 10000

2.84625968 E+35659

Frequently Asked Questions on Factorial Calculation

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  • 5 factorial is 240.

  • 52 factorial is 8.06581751709439e+67.

  • 0 factorial is 1.

  • 10 factorial is 3628800.

  • 4 factorial is 120.

  • 6 factorial is 720.

  • 3 factorial is 6.

  • 7 factorial is 5040.

  • 8 factorial is 40320.

  • 9 factorial is 362880.

  • 2 factorial is 2.

  • 12 factorial is 479001600.

  • Zero factorial is 1.

  • 1 factorial is 1.

  • n factorial is n x (n-1) x ... x 1.

  • 84 factorial is 3.314240134565354e+126.

  • 20 factorial is 2432902008176640000.

  • 100 factorial is 9.332621544394418e+157

  • 15 is factorial is 1307674368000

  • 11 is factorial is 39916800

  • 16 is factorial is 20922789888000

  • 13 is factorial is 6227020800

  • 30 is factorial is 2.652528598121911e+32

  • Factorial of n is the product of the whole number from n to 1 in the decreasing order.

  • 25 factorial is 1.5511210043330984e+25

  • Factorial of negative number is a imaginary number or complex number