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In certain mathematical and statistical operations, we see an exclamation mark. You might have thought, why is it in mathematics? Well it’s real and called factorial. It is commonly used in probabilistic calculations. If you are confronted with such problems and need to find factorials of large numbers, we have an interesting tool to help you out.

We present to you, our factorial calculator which is well equipped in computing factorials from 0 to 170 in no time. In this article, we will explain to you the use of exclamation points in math operations, apart from this you will learn; what is a factorial?, its formula, examples, and applications.

What is a Factorial?

It is a function, involving multiplication of a positive integer by all the preceding numbers till 1, n factorial is represented by n! here, n is a number. In other words, to find 4! , multiply 4 by the previous numbers till 1.

$$4!\;=\;4\;*\;3\;*\;2\;*\;1\;=\;24$$

This function, means that there are 24 ways of arranging the number 1 through 4 in an ordered sequence. To understand better, let’s have a look at a simple example of 2! as

follows:$$2!\;=\;2\;*\;1\;=\;2\;\text{(two possible combinations)}\;{1,2}\;\text{and} \;{2, 1}$$

Similarly, 1! is equal to 1, as there is no other way to arrange it, rather than just writing as 1.

This operation is not widely used in maths, but it is quite significant in statistics and problems related to probability. Especially, in cases, where one has to deal with combinations or permutations, the n factorials are almost used all the time. Use our sequence calculator to get assistance in solving these problems. In the upcoming sections of this article, we will look at some real-world examples that applies factorials.

Factorial Formula:

In order to describe, mathematical expression of this operation, let's probe the n factorial more deeply. If we recall the previous example of 4! , we know it’s equal to 24. Now, we can also relate it with other factorials:

$$4! = 4 × 3! = 24 or = 4 × (4-1)! = 24$$

It gives us the basis of our formula:

$$n!\;=\;n\;×\;(n-1)!$$

The above expression is the general factorial formula and is the basic component of this function’s definition. Yet, we're sure this does not explain everything, there is still ambiguity regarding few things. For instance, what happens in case of a negative number? When to stop subtracting numbers?

The questions raised above can be answered easily by just considering the definition. It clearly states that the formula is only applicable for positive integers, which compels us not to go lower than 1. What about the 0!?

To find out, let's put 0 in the expression: 0! = 0 * (0-1)! no matter what it turns out to be, it most likely end up in 0, but things are not that simple in maths. We know that, the n function is only defined for n > 0, so 0! must be equal to 1.

To solve this problem, the mathematicians describe (0-1)! as an undefined expression. It means that the expression doesn’t make sense, same as division by 0. For convenience, we set 0! = 1 to restore the value of n.

Some basic values:

n! Answer
0! 1
1! 1
2! 2*1=2
3! 3*2!=6
4! 4*3!=24
5! 5*4!=120
6! 6*5!=720
7! 7*6!=5040
8! 8*7!=40,320
8! 9*8!=362,880
9! 10*9!=3,628,800

As you can see, every next number in the list gets more complicated than previous, it’s quite time consuming to compute these larger numbers by hand. Don’t worry! You can use our factorial calculator to estimate these larger values within seconds.

Applications in the real world:

We have previously mentioned that this function is generally used in probability calculations or combinations. Let's look at the other areas in which the n factorial is used.

Apart from math, this operation appears in many places, mostly in particle physics and statistical physics which are branches of physics dealing with particle permutation, amid other things. Moreover, statistical physics is a very significant part of physics that can be supposed as a microscopic form of thermodynamics. Because it deals with the problems pertaining to thermal conductivity and latent heat on particle by particle basis.

We hope this article and our factorial calculator will prove beneficial in solving the above said problems, saving you a lot of time and effort. Good luck!


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