**Math Calculators** ▶ Factorial Calculator

This free online factorial calculator helps you to calculate the factorial of given n numbers. Also, the factorials calculator calculates the factorial as well as does the following arithmetic operations on the factorial of two numbers:

- Addition.
- Subtraction.
- Multiplication.
- Division.

Give a complete read to this important and useful content, we’ve definition, formula, how to calculate a factorial manually and different other useful terms related to our topic.

Read on!

The formula used by this online factorial calculator, is as follow:

$$ n! = n \times (n−1) \times (n−2) \times ……. \times 1 $$

Where,

\(n\) is the desired number for which you want to do the calculations.

Consider this free prime factorization calculator that helps to make prime factors of any number, create a list of all prime numbers up to any number.

The formula clearly shows that it could only apply to the positive numbers which bounds us not to go below \(1\). As it gives the number of ways to permute the object, so you can’t have an object less than zero \((0)\).

First of all, keep in mind that the \(0!\) is equals to one \((0! = 1)\). It looks like some mistake but it is the fact, that’s why it is a special case. Now we will go deep into this logic:

The problem that arose when we going to calculate the factorial of \(0\) is that:

\(0!\) = \(0! \times (0-1)!\)

We know that the factorial of \(n\) is only defined when \(n>0\) so that’s why we have a problem. The term \((0-1)!\) gives the undefined results in mathematics and have no meaning the same as when divided by zero. The problem is not that we cannot calculate it; the problem is that it doesn’t have any meaning. If we place the value of \(0!\) to \(1\), we can get the expected values for \(n!\). Our factorial calculator determines the factorial of zero and other positive integers as well.

Calculating factorials becomes very easy with this free factorial calculator which determines the accurate results of the numbers given.

Read on!

To find \(n!\), just follow the given steps:

**Inputs:**

• First of all, enter the number for which you want to show the resut in the designated field.

• Then, hit the calculate button.

**Outputs:**

Once you enter in the field, the calculator shows:

• Factorial of the number.

• Step-by-Step calculations.

To do the arithmetic operations on the factorial of given numbers, just stick to the following points:

**Inputs:**

• First of all, enter the first number.

• Very next, plug-in the second number.

• Finally, hit the calculate button.

**Outputs:**

The calculator shows:

• Factorial of the both numbers.

• Arithmetic operation on the factorial of two numbers according to the selected option.

• Step-by-Step calculations.

The formula used for the calculation between the numbers is as follow:

$$ n! = n \times (n−1) \times (n−2) \times ……. \times 1 $$

Where,

\(n\) is the number.

Let’s have examples for each method to clearly understand the concept with complete step-by-step calculations.

Let’s have an example:

**For example:**

Calculate the factorial of \(8\)?

**Solution:**

Here, \(n = 8\)

**Step 1:**

\(8! = 8 \times (8−1) \times (8−2) \times (8−3) \times (8−4) \times (8−5) \times (8−6) \times (8−7)\)

**Step 2:**

\(8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)

**Step 3:**

\(8! = 40320\)

For the addition, we have an example:

**For example:**

Add the factorial of \(3\) and \(4\)?

**Solution:**

Here, \(n = 3\)

\(m = 4\)

**Step 1:**

Find \(n! = 3\)

\(3! = 3 \times (3−1) \times (3−2)\)

\(3! = 3 \times 2 \times 1\)

\(3! = 6\)

**Step 2:**

Find \(m! = 4\)

\(4! = 4 \times (4−1) \times (4−2) \times (4−3)\)

\(4! = 4 \times 3 \times 2 \times 1\)

\(4! = 24\)

**Step 3:**

\(n! + m! = 6 + 24\)

\(n! + m! = 30\)

For the subtraction, we have an example:

**For example:**

Subtract the factorial of \(5\) and \(3\)?

**Solution:**

Here, \(n = 5\)

\(m = 3\)

**Step 1:**

Find \(n! = 5\)

\5! = 5 \times (5−1) \times (5−2) \times (5−3) \times (5−4)\)

\(5! = 5 \times 4 \times 3 \times 2 \times 1\)

\(5! = 120\)

**Step 2:**

Find \(m! = 3\)

\(3! = 3 \times (3−1) \times (3−2)\)

\(3! = 3 \times 2 \times 1\)

\(3! = 6\)

**Step 3:**

\(n! – m! = 120 – 6\)

\(n! – m! = 114\)

For multiplication, we have an example:

**For example:**

Multiply the factorial of \(7\) and \(4\)?

**Solution:**

Here, \(n = 7\)

\(m = 4\)

**Step 1:**

Find \(n! = 7\)

\(7! = 7 \times (7−1) \times (7−2) \times (7−3) \times (7−4) \times (7−5) \times (7−6)\)

\(7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)

\(7! = 5040\)

**Step 2:**

Find \(m! = 4\)

\(4! = 4 \times (4−1) \times (4−2) \times (4−3)\)

\(4! = 4 \times 3 \times 2 \times 1\)

\(4! = 24\)

**Step 3:**

\(n! \times m! = 5040 \times 24\)

\(n! \times m! = 120960\)

For division, we have an example:

**For example:**

Divide the factorial of \(5\) and \(6\)?

**Solution:**

Here, \(n = 5\)

\(m = 6\)

**Step 1:**

Find \(n! = 5\)

\(5! = 5 \times (5−1) \times (5−2) \times (5−3) \times (5−4)\)

\(5! = 5 \times 4 \times 3 \times 2 \times 1\)

\(5! = 120\)

**Step 2:**

Find \(m! = 6\)

\(6! = 6 \times (6−1) \times (6−2) \times (6−3) \times (6−4) \times (6−5)\)

\(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1\)

\(6! = 720\)

**Step 3:**

\(\frac {n!}{m!} = \frac {120}{720}\)

\(\frac {n!}{m!} = 0.16666\)

You can use our factorials calculator to verify all of the examples, that done all the calculations according to the factorial formula and determine the speedy results accurately.

It can be defined as “a number which is the product of all the positive integers less than or equal to the number \(n\)”. It is represented by an exclamation sign \((!)\). In simple words, it is a function which multiplies the number with every number below it.

It is a number determine by multiplying its ‘minus one’, then ‘minus two’ and so on till 1. It is denoted as \(n!\).

The excel uses the function of \(=FACT\) , to calculate the factorial of the given number.

Itis a mathematical expression, indicted by the exclamation mark “\(!\)”. You must multiply all the numbers that exist between the numbers to calculate the factorial of number.

As the formula is \(n(n-1)!\) means n times \((n-1)!\). So, smaller is the factor of the larger factorial \(N\).

You can answer this question by multiplying \((k+1)!\) by \(2\).

The factorial of the number can be helpful in Statistics to determine the permutation and combination of the numbers. Also, when it comes to Calculus, it determine the Taylor series, Binomial theorem for symmetrization the operations & derivative of nth function and many more. Simply, you can use this online factorial calculator which helps the students as well as professionals to compute the factorial of the numbers.

Let’s check out the given table.

Factorial | Answer |
---|---|

n! | n(n-1)…1 |

0! | 1 |

1! | 1 |

2! | 2 |

3! | 6 |

4! | 24 |

5! | 120 |

6! | 720 |

7! | 5040 |

8! | 40320 |

9! | 362880 |

10! | 3628800 |

12! | 479001600 |

15! | 1307674368000 |

20! | 2432902008176640000 |

45! | 1.1962222086548E+56 |

50! | 3.0414093201713E+64 |

100! | 9.3326215443944E+157 |

From the source of Wikipedia: Factorial, Definition, Rate of growth and approximations for large n, and much more!

The source of khanacademy: n! function (all you need to know about it)

The xaktly site provides: The role of factorials in math (ultimate guide)

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