These are two major questions that the students need to answer when they are dealing with this topic. In generic terms, if there is a number “n”, its factorial would be a product of all the numbers which have a value of less than or equal to “n”. Consider an example where the value of n is 4. Thus, the factorial of 4 would be given as.
As “n” = 4, n! is given as
\(4\times3\times2\times1\)
\(n! = 24\)
Our advanced factorial calculator stands out in every aspect of the scientific calculator to find the factorial of a number. It is easy to use and the accuracy of results is not compromised in any manner. Here are the steps you have to perform to use this tool and determine factorial.
To start with, enter the first number for which you have to calculate the factorial. Consider that you want to calculate the factorial of 6. Once you have entered the number, click the calculate button and you would see the output on the right side of the screen. In the outputs section, you would see two parts. The first would show you the answer. For instance, in this case, you are calculating the factorial of 6 so the answer would be 720. Now, a lot of people would want to see how the answer was calculated. This is where the second section comes into play. This part shows you how the answer was calculated. In this case, the value of 6! Is given as.
\(6\times5\times4\times3\times2\times1 = 720\)
When you click the tab titled “advanced factorial option”, a drop-down menu would appear. This is where you have to provide information for the second number. First of all, select the mathematical operation which has to be performed. You can choose from subtraction, addition, division, and multiplication with this factorial calculator. After that, enter the second number for which the operation has to be completed. Consider that it is “4” in this case. Along with that, let us reconsider the first number as 6 and opt for the subtraction option.
In mathematical terms, this option would be \(6! - 4!\)
The outputs would be shown to you after you have clicked the “calculate” button. In the first row, the factorial of the first number and its calculation process would be shown. In this case, it would be 6! which carries a value of 720. The second portion would show how it was determined.
\(6! = 6\times5\times4\times3\times2\times1 = 720\)
In the second row, the factorial of the second number would be shown along with its calculation process. In this example, the second number is 4. Thus, its factorial process would be
\(4\times3\times2\times1 = 24\)
The last row would show the result of the mathematical operation.
In this case, it would be \(6! - 4!\)
The formula of factorial has a simple logic behind it. For instance, consider that you have a number “b”, how would the factorial of this number be determined? It would be given.
b! = b (b-1) (b-2)………
If you have a look at the implementation of the formula of the factorial calculator, it explains that the factorial of a number is a product of all the numbers that are less than or equal to it.
Let's suppose to find the factorial of 10.
\(10! = 10\times9\times8\times7\times6\times5\times4\times3\times2\times1\)
\(10! = 3628800\)
Similarly, if you want to determine the factorial of 8, the value would be
\(8\times7\times6\times5\times4\times3\times2\times1\)
\(8! = 40320\)
Normally, people have a lot of confusion about what the factorial of 0 is.
Consider that you have a number “n” and its factorial has to be determined. The factorial would be given.
\(n! = n(n-1)!\)
Consider that \(n = 1\) and insert this value in the formula given above to find the factorial of 0.
\((n-1)! = \dfrac{n!}{n}\)
\((1-1)! = \dfrac{1!}{1}\)
\(0! = 1\)
Analysis of results and formula used by factorial expression calculator.
If you have a glance at the formula mentioned above of the advanced factorial calculator, the value of 0! Is 1. This series of calculations basically shows how the value of 0! can be determined. In other words, the core logic is explained through this example.
| 1 | 1 |
| 2 | 2 |
| 3 | 6 |
| 4 | 24 |
| 5 | 120 |
| 6 | 720 |
| 7 | 5040 |
| 8 | 40320 |
| 9 | 362880 |
| 10 | 3628800 |
| 11 | 39916800 |
| 12 | 479001600 |
| 13 | 6227020800 |
| 14 | 87178291200 |
| 15 | 1307674368000 |
| 16 | 20922789888000 |
| 17 | 355687428096000 |
| 18 | 6402373705728000 |
| 19 | 121645100408832000 |
| 20 | 2432902008176640000 |
| 21 | 551090942171709440000 |
| 22 | 1124000727777607680000 |
| 23 | 25852016738884976640000 |
| 24 | 620448401733239439360000 |
| 25 | 15511210043330985984000000 |
| 26 | 403291461126605635584000000 |
| 27 | 10888869450418352160768000000 |
| 28 | 304888344611713860501504000000 |
| 29 | 8841761993739701954543616000000 |
| 30 | 265252859812191058636308480000000 |
| 31 | 8222838654177922817725562880000000 |
| 32 | 263130836933693530167218012160000000 |
| 33 | 8683317618811886495518194401280000000 |
| 34 | 295232799039604140847618609643520000000 |
| 35 | 10333147966386144929666651337523200000000 |
| 36 | 371993326789901217467999448150835200000000 |
| 37 | 13763753091226345046315979581580902400000000 |
| 38 | 523022617466601111760007224100074291200000000 |
| 39 | 20397882081197443358640281739902897356800000000 |
| 40 | 815915283247897734345611269596115894272000000000 |
| 41 | 33452526613163807108170062053440751665152000000000 |
| 42 | 1405006117752879898543142606244511569936384000000000 |
| 43 | 60415263063373835637355132068513997507264512000000000 |
| 44 | 2658271574788448768043625811014615890319638528000000000 |
| 45 | 119622220865480194561963161495657715064383733760000000000 |
| 46 | 5502622159812088949850305428800254892961651752960000000000 |
| 47 | 258623241511168180642964355153611979969197632389120000000000 |
| 48 | 12413915592536072670862289047373375038521486354677760000000000 |
| 49 | 608281864034267560872252163321295376887552831379210240000000000 |
| 50 | 30414093201713378043612608166064768844377641568960512000000000000 |
(n+1)! = (n+1)(n)(n−1)(n−2) …… (n−n+1)
Factorial (100) = 9.332622e+157
5 × 4 × 3 × 2 × 1 = 120
Factorial of 5 = 120
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
Factorial of 9 = 362,880
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