## What is a Factorial?

As per the factorial definition the factorial is the procuct of all positive integers which are less than or equal to zero. Factorial value of 0! is 1. Factorial Sequence calculator works on the same principle.

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. If your calculation brought an error, learn more by using Percent Error Calculator. To understand better, let's have a look at a simple example of 2! as

follows:

$$2!\;=\;2\;*\;1\;$$

2**(two possible combinations)**1,2 and 2,1

Similarly, 1! is equal to 1, as there is no other way to arrange it, rather than just writing as 1. You can use Scientific Notation Calculator & Arithmetic Sequence Calculator for similar yet different calculations.

## What is Factorial formula?

As per above 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. For formula related math calculations, try Distance Formula Calculator & Quadratic Formula Calculator.

Yet, we are 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?

## Why is it not possible to have a negative Factorial?

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.

You can also learn & practice by using our Integral Calculator & Derivative Calculator as well.

## Factorial Table:

Factorial | n! | Answer |
---|---|---|

0 factorial | 0! | 1 |

1 factorial | 1! | 1 |

2 factorial | 2! | 2*1=2 |

3 factorial | 3! | 3*2!=6 |

4 factorial | 4! | 4*3!=24 |

5 factorial | 5! | 5*4!=120 |

6 factorial | 6! | 6*5!=720 |

7 factorial | 7! | 7*6!=5040 |

8 factorial | 8! | 8*7!=40,320 |

9 factorial | 9! | 9*8!=362,880 |

10 factorial | 10! | 10*9!=3,628,800 |

As you can see, every next number in the list gets more complicated than previous, it takes a lot of time to compute these numbers by hand. You can use our factorial calculator to estimate these larger values within seconds.

## What is a Factorial calculator?

As the values of factorials continue to rise, it becomes difficult to solve it manually. There are many factorial calculators available online to solve factorial without spending a lot of time.

These factorial calculators are usually reliable and accurate as they produce result effiently.

## How to use Factorial calculator?

Our factorial calculator is very easy to use. What you need to do is to give your value in the field and it will quickly give you the accurate result.

We also have other math related calculator like Mean Calculator, Midpoint Calculator & Sig Fig Calculator which you can use for your practice.

I hope you liked our factorial sequence calculator and its article. Send us your feedback so that we could improve if required.