Factorial Calculator
Calculate Factorial of a number. Learn more about 0 factorial, 100 factorial, negative factorial and formula for calculating n factorial
Find the factorial of the given number
Factorial is
CopyWhat is a Factorial?
Definition 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 = 6Notation
Factorial of a number is denoted by the exclamation symbol (!) followed by the number.(x!) or Fact(x)
Example: 15! or Fact(15)Factorial Formula:
(factorial of n) n! =n x (n-1) x (n-2) x ....1 = n x (n-1)!
According to our formula, if n =5, then
5! = 5 x (5-1) x (5-2) x (5-3) x..1
5! = 5 x 4 x 3 x 2 x 1
5! = 120Factorial example:
1! = 1
2! = 2x1 = 2
3! = 3x2x1 = 6
4! = 4x3x2x1 = 24
5! = 5x4x3x2x1 = 120Factorials grow very rapidly. 2! is 2,
3! is 6,
5! is 120,
10! is over 3.6+ million and
15! is 1.3 x 10^12 which is million of million.The largest factorial that can be calculated on a standard computer is 170!.
How to Use the Factorial Calculator?
- Simply enter the number for which factorial is required in Input field
- The factorial for that number is displayed in the output box automatically as you complete the input.
The factorial calculator tool is simple to use.
Note: The maximum allowed input is 170.
What is 0 Factorial?
Zero Factorial 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?
No, there is no negative factorial.
Factorials are defined only for non-negative integers. For example, the factorial of 1 is 1, 4 is 24 and so on. The factorial of -1 or -n 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 3! ways to arrange 3 different objects in a row. However, same does not make sense for a -ve factorial
Table of Factorials
| 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
Yes, Factorials grow much faster than exponents.
Exponential growth is 2 ^ n or any base ^ n where the base can be 2, 3, 5 , 10 or any number. The number remains the same and only the power is multiplied 'n' number of times.
Factorial growth uses higher and higher numbers with every increment. Initially, it appears as a small growth but quickly reaches infinity. For eg from 5! to 10! it goes from 120 to 3 million.
No, Iteration is always faster than recursion. Recursion can be more efficient in terms of programming but iteration is simpler and performs better.
A recursion is when a function calls itself within itself continuously till it exits the processing loop under some condition
In terms of memory, the recursion uses more memory as each call of the function is pushed to a stack till the entire computation is completed. It can go out of memory if the computation is big.
In iteration, the function is invoked or computation is done inside a loop for a definite count.
Every factorial can be expressed in terms of another factorial. As it's a repetitive pattern, it's efficient to use a recursive function to compute factorials.
for eg 100! = 100 x 99!
25! = 25 x 24!
5! = 5x4!
2! = 2 x 1!
You can calculate factorial by Iterative Method or Recursive Method
To find the factorial of a given number with iterative method , multiply the number with all previous numbers till 1.
This will be done in a loop
To find the factorial of a given number using Recursive method,
create a recursive function that returns the product of the given number with the output of the recursive function which takes n-1 as the input.
it returns 1 when the input to the recursive function is 0.
