You might know about the Factorial Concept in Mathematics where a series of numbers are multiplied with each other to get the target result. However, you will be surprised to know that the โFactorial in JavaScriptโ can also be done with some simple tricks.
Not only in JavaScript but the Factorial can also be done in various programming languages. But there is a unique difference present in JavaScript than any other programming language to get the Factorial Number.
This article is going to discuss the steps needed to Get Factorial in JavaScript along with some limitations for the same. Still, if you have any doubts related toย JavaScript homeworkย then you can hire the best experts from CodingZap.
Summary or Key Highlights:ย
- The Factorial is a complete Mathematical Concept & has no direct link with Programming.
- JavaScript can get the Factorial just like other Programming Languages.
- There are two different ways present to Get Factorial in JavaScript.
- JavaScript has a Limitation to Get Factorial of every number.
- Above a Certain Integer Value, you have to use tricks to get JavaScript Factorial.
What is Factorial? Read Below
Factorial is a concept that comes from Mathematics. In Mathematics, we all know about the Permutation & Combination concept. Getting the factorial of a number belongs to that section of Mathematics.ย
We can say it is a series of multiplication of numbers.ย In mathematics, the factorial of an integer x is the product of all positive integers less than equal to x, where x is a natural number.
Is there an issue in understanding the direct principle of the factorial theory? Let us have a look at the following logic.
Factorial logic:ย let the number be x. Therefore, x!= x(x-1)*(x-2)*(x-3)*โฆ.*1
For example, the factorial of 5! is 120. By definition 5!=5*4*3*2*1=120
How to Calculate Factorial In JavaScript?
In JavaScript, to Calculate the Factorial of Integer Values, you have to use any one of the following methods. There are two different ways present for Factorial Calculation in JavaScript. One is the Iterative Method & another is the Recursive Method.
In the Iterative Method, you can use any Loop Concept of the JavaScript Programming Language. You can use the For Loop, While Loop, etc. We are going to first discuss the Factorial Calculation Method in Iterative Approach.
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Calculate Factorial In JavaScript Using Iterative Approach:
Now, in this Iterative Approach, the For Loop will be used to get the required result. Instead of the For Loop, you can use the While Loop & Do-While Loop as well. But in that case, the Logic of the Problem will be different.
You might find the following logic similar to the Factorial of Different Other Programming Languages. If you need, you can alter the code as per your own.
// Function to calculate the factorial of a number using javascript
function factorial(y) {
var num=0,i=0,fact=1;// Declaration Of Variables
num=y;
for(i=1;i<=num;++i){// For Loop from 1 to less than the x value.
fact=fact*i; //logic
};
console.log("The Factorial Is: " + fact); //output on console.
}
// assign a value to x for finding the factorial of a number using javascript
var x=5;
//pass the value of x to the function factorial by calling it.
factorial(x);
Steps Of The Program:
- In the first code, the factorial function has been declared in JavaScript.ย
- Inside that new function, some local variables have been declared & assigned some values.
- Then, a For Loop will be executed from 1 until the appearance of the input number.ย
- In each iteration of the For Loop, the series of numbers will be multiplied from 1.
- In the end, the value will be printed using the Console Log.
- In the lower code, the process of providing user input will develop in the program.ย
- One integer value will be provided that will be shared as an argument value to the function.
Output:ย
Now, from the above output, we can see that the Factorial Result is coming as 120. And the 120 is the Factorial Value of the Integer 5. So, the program is executing completely fine & there is no error present in the code.
Calculate Factorial In JavaScript Using Recursive Approach:
Now, as the Iterative Method is completed, let us have a look at the Recursive Approach. In this process, we will declare one function that will call itself multiple times to get the required solution. This is a good approach for such a problem.
We will use the same integer value as the above to get a similar result. This will help to analyze the code easily.
let n = 5; // Taking The Number
function fact(n) {
if (n === 0) { // Implementation Of Base Case To Get Factorial N Numbers
return 1;
}
else {
return n * fact( n - 1 ); // Recursively Calling Function To Get Factorial N Numbers
}
}
console.log("The Factorial Of 5 Will Be: " + fact(n)); // Printing The Output
Steps Of The Program:ย
- Now, the Integer Value will be taken in the Program as Number 5.
- Now, the Function Fact() will be declared that will take the Number as an Argument.
- We will implement an End Case in the Program.
- Also, we will implement the Recursive Call at the ending line of the function.
- At last, we will print the value of the Result.
Output:ย
From the above output, we can notice that it is completely similar to the above Iteration Method. So, the Recursion Method is the same useful as the Iterative Method. There is no Bug in this Program as well, so it can be easily used.
What Is The Limitation To Calculate Factorial In JavaScript?
From all of the above discussion, we have learned the Implementation Process of Factorial in JavaScript. As a result, the function works fine till the value of x=21 but fails once we go beyond the x value greater than 21.
For example, letโs find the factorial of 22ย using the above function.
Have a look at the output above where we try to find the factorial of x=22 which is greater than 21.
Furthermore, you can see that the output of factorial 22! should be 1.1240007277776077e+21 but the actual answer should be 1124000727777607680000.
Doesn’t it seem like a crazy move by JavaScript? Is there any problem we are having? Or it is the default JavaScript problem? Let us try to know it.ย
Also, while studying Python the programmer needs to declare the data type before declaring one variable. And, this is done using type conversion.
Why JavaScript Canโt Calculate Factorial Of Large Integers?
Our factorial logic is correct so it must have some problem with JavaScript for storing very large values.
Here is the reason why-
JavaScript Numbers Are Always 64-Bit Floating Point
In other programming languages, we find a large set of numbers. Like, integer numbers, float numbers, double numbers, etc. But inside JavaScript, there is no such large set of numerical data. Here in case of the JavaScript, all numbers are assumed as double precision numbers.
So, one can face such issues while using JavaScript programming language. It is not the fault of the developer, but a problem with the compiler. That is the reason; we are getting issues while counting the factorial of N numbers.
Integers (Numbers Without A Period Or Exponent Notation) Are Accurate Up To 15 Digits
Another major issue, in this case, is the integer precision problem of JavaScript. In JavaScript, only 15 digits are allowed in any integer variable. If any integer variable has up to 15 digits element, it will work normally. Having more digits, it will start malfunctioning.
Sometimes, the decimal value goes to 17 digits, if there is more than 15 digits are present in any number. So, these are the key factors we should consider while doing factorial of N numbers.
How To Overcome Limitation In JavaScript To Calculate Large Factorial Values?
From all the above discussion, you should have understood that the major problem in JavaScript to Calculating the Factorial of any Large Number. So now, it is time to overcome the problem by implementing a simple JavaScript Program.
The Program will be long enough, however with this program. You can get the factorial of every number, whether it is a large number or a small number. Do check the following steps of the program to understand the concept very easily.
function add(str1, str2) {
let sum = ""; // our result will be stored in a string.
//We'll need these in the program many times.
let str1L = str1.length;
let str2L = str2.length;
// if s2 is longer than s1, swap them.
if(str2L > str1L ){
let temp = str2;
str2 = str1;
str1 = temp;
}
let carry = 0; // number that is carried to the next decimal place, initially zero.
let a;
let b;
let temp;
let digitSum;
for (let i = 0; i < str1.length; i++) {
a = parseInt(str1.charAt(str1.length - 1 - i)); // get ith digit of str1 from right, we store it in a
b = parseInt(str2.charAt(str2.length - 1 - i)); // get ith digit of str2 from right, we store it in b
b = (b) ? b : 0; // make sure b is a number, (this is useful in case, str2 is shorter than str1
temp = (carry + a + b).toString(); // add a and b along with carry, and store it in a temp string.
digitSum = temp.charAt(temp.length - 1); // least significant digit
carry = parseInt(temp.substr(0, temp.length - 1)); // carry
carry = (carry) ? carry : 0; // if carry is not a number, make it zero.
sum = digitSum + sum; // prepend digitSum to sum string
}
if (carry) { // if carry is non-zero after loop ends
sum = carry.toString() + sum;
}
return sum;
}
function extraLongFactorials(n) {
let fact = "1";
for (let i = 2; i <= n; i++){
if(Number.isSafeInteger(parseInt(fact) * i)){
fact = (parseInt(fact) * i).toString();
} else {
// fact = fact + fact + .. i times
let factxi = "0"; // this is (fact * i) for us.
for(let j = 0; j < i; j++){
factxi = add(factxi, fact);
}
fact = factxi; // update the value of fact before continuing the loop.
}
}
return fact;
}
console.log("Factorial Of Value 25:" + extraLongFactorials(25)); // prints 15511210043330985984000000
console.log("Factorial Of Value 34:" +extraLongFactorials(34)); // prints 295232799039604140847618609643520000000
Steps Of The Program:ย
- The above code is nothing but a simple factorial definition in JavaScript. We have followed the simple iteration rule to implement the program. We have made some small changes to the program.
- Inside of it, we have used isSafeInteger() function. It is used to check the number that is going to be used to find whether factorial is safe or not. It checks whether the number is all right to move further or not. If it is OK, then we will move with the normal iteration method.
- If the number is not normal, then it will be treated as the string element. Multiplication will be done with the help of another function add(). The implementation of the function is following.
- Now, we should take two different numbers in the string format as the argument of the function.
- Now, the length of each string will be calculated. And the String which is longer will be kept on the top & the smaller one will be kept low to that. If needed, we have to do some swapping of the strings.
- Now, one for loop will be implemented & the for loop will work on the longest string data. Each & every digit of both strings will be calculated. As per the need of the calculation, the carry should be marked.
- After every iteration, the leftmost element will be added to the โSumโ string. And the remaining one will be added to the โCarryโ string. Here, we should note that the โSumโ string is the return variable.
- At the end of the program, the need to use the โCarryโ will be finished. The work will be done on the โSumโ part. The sum will be the result of the add() function.
Output:ย
Conclusion:
As we can see, the Calculation of โFactorial in JavaScriptโ is more tricky than other programming languages.
It is recommended to Clear the Basics of JavaScript first before moving to Intermediate Concepts like Factorial Calculation. Finally, thanks for reading, if the tutorial was helpful to you feel free to comment, and donโt forget to share.
if you are working towards becoming a better JavaScript developer you can readย JavaScript and jQuery.
So, hope you have liked this piece of article. Share your thoughts in the comments section and let us know if we can improve more.
Takeaways:
- The Factorial Calculation in JavaScript is not as simple as other Programming Languages.
- There is also an Iterative & Recursive Manner in JavaScript to get Factorial.
- In the Iterative Method of Factorial, For Loop, While Loop, etc. can be used.
- The JavaScript can find a Factorial of Numbers larger than the Value 21.
- We have to use some tricks to get the Factorial of Larger Numbers as in JavaScript, the Numbers are seen as the 64-bit Floating Point Value.
