The number of digits in the factorial 100 is **158**

### Detailed answer:

- 100! It is exactly: 9332621544394415268169923856267004907159682643816214685929638959993229915608941463976156518286253697920820827222237223722372237223722222222222222222
- The approximate value of 100! is 9.3326215443944E+157 .
- The number of zeros at the end of 100! is 24 .
- The number of digits in 100 factorial is 158 .
- The factorial of 100 is calculated, through its definition, in this way:

Today we are going to see **how the factorial of a number is calculated** . Calculating factorials is very simple, let’s see what it consists of:

## negative number

The factorial of a negative number does not exist, since they only work based on natural numbers.

## factorial properties

**The factorial of a number can be expressed in terms of another factorial.**

Example:

5! = 5 x 4!

10! = 10 x 9 x 8!

25! = 25 x 24 x 23 x 22!

** in general** :

**n! = nx (n-1) x (n-2) x (n-3) x (n-4)!**

Example:

## What is the factorial function?

The factorial function is represented by an exclamation point “ **!” **behind a number. This exclamation means that you have to multiply all the positive integers between that number and 1.

**For example:**

To this number, **6! **we usually call it “ **6 factorial** ”, although it is also correct to say “ **factorial of 6** ”.

On your calculator you will see a key with “n!” or “x!”. This key will help you to directly calculate the factorial of the number you want.

## Some Examples of Factorials

Let’s see some more examples of factorials:

As you see, 100! it’s huge…

And what do we do with the smaller numbers? 1 factorial is logically 1, since we multiply 1 x 1:

But how can we calculate the 0 factorial? Well, this doesn’t make sense when we apply the rule that you have to multiply all positive integers between 0 and 1, since 0 x 1 is 0.

In the end, by convention it has been agreed that the most useful thing is that the 0 factorial is equal to 1. So remember:

## What can we use factorials for?

Factorial numbers are used mostly in **combinatorics** , to calculate combinations and permutations. Through combinatorics, factorials are also often used to compute probabilities.

Let’s see a simple example of a problem in which we can apply the factorials:

In this problem we are being asked what is called a **permutation** , that is, that we find out all the possible ways in which these 4 cards can be combined **taking into account the order** in which we place them.

If we start by making all possible rows starting with the ace of diamonds, we can make 6 combinations:

We will also have 6 possible combinations with the clubs, the hearts and the spades, that is, 6 combinations starting with each of the 4 cards: 4 x 6 = 24

Using the factorial function, we could have solved the problem much more easily:

We think of a single combination of the **4 aces** :

– When we have chosen the first one, **we only have 3 left** to choose from

– When we have chosen the second, **we only have 2 left** to choose from

– When we have chosen the third, **we only have 1 left** to choose

**Therefore, all possible combinations will be 4 x 3 x 2 x 1.**

**Or what is the same, 4! = 24**

### What is the factorial of a natural number?

The **factorial of a** positive integer is defined as the product of all the **natural numbers** before or equal to it.

### What is a factorial and how is it calculated?

The **factorial function is** represented by an exclamation point “!” behind a **number** . This exclamation means that you have to multiply all the positive **integers** between that **number** and 1. To this **number** , 6! we usually call it “6 **factorial** ”, although it is also correct to say “ **factorial** of 6”.

### What is the factorial of a number in statistics?

The **factorial** function is a mathematical formula represented by the exclamation mark “!”. In the **Factorial** formula , all the integers and positive numbers between the number that appears in the formula and the number 1 must be multiplied.

### What is 5 factorial?

Factorial

3 | 6 |

4 | 24 |

5 | 120 |

6 | 720 |

7 | 5040 |

16 more rows

### How to calculate the factorial of a number in algorithm?

### What is the value of 50 factorial?

The **factorial** of **50 is** equal to 3.0414093201713E+64.

### What is the factorial number of 6?

Factorial

5 | 120 |

6 | 720 |

7 | 5040 |

8 | 40,320 |

9 | 362,880 |

16 more rows

### How much is a factorial?

- So, to find how much a factorial is worth, the following sequence must be done on the calculator: Normally, CASIO calculators have the factorial key x! on! above the x-1 button. As an example, we are going to solve a factorial with the calculator so that you can verify that you know how to do it.

### What is the factorial in mathematics?

- The factorial is also used in mathematics to determine the Taylor polynomial of a function. Likewise, the factorial is used to solve some combinatorics problems, specifically it is used to calculate combinations and permutations.

### How to calculate the factorial of 4?

- Therefore, to calculate the factorial of 4 we have to multiply the numbers 1, 2, 3 and 4: So that the factorial of 4 results in 24. To finish understanding the concept of factorial of a number, we leave you as example the calculation of several factorials of different numbers:

### What are the properties of the factorial number?

- Properties of the factorial number The factorial number complies with the following characteristics: Being two positive integers n and m such that n is greater than m, then, obviously, the value of the factorial of n is greater than the value of the factorial of m.