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Factorial Calculator

Factorial Calculator

Calculate Factorials using:

Find n!

n!

m!

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An online factorial calculator helps to calculate factorial (n!) of a given n positive number. Also, you can be able to add, subtract, multiply, and divide factorial of two numbers by using the factorial finder calculator.

Here for you, we have a factorial definition, how to calculate it, and some essential content that might work best for you!

What is a Factorial?

In mathematics, the factorial function (!) are said to be as the products of every positive number from 1 to n.
For example: If n = 5, then 5! is n ! = 1 * 2 * 3 * 4 * 5 = 120. If n = 7, then 7! is 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040.

Well, you can also find the number of possible combinations from the large dataset by using an online combination calculator. And, if your concern is to determine the number of possible subsets from different orders, then a permutation calculator is the best way to go!

Factorial Formula:

The given formula helps you to calculate factorials:

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

Where,

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

Also, you can simply add the positive number into an online factorial calculator and lets it simply factorials within seconds.

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.

Why is it Not Possible to Have a Negative Factorial?

The factorial formula clearly shows that it could only apply to the positive numbers which bound 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 \((0)\).

The Factorial of Zero (0!) is a Special Case:

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 where the confusion takes place. The term \((0-1)!\) gives the undefined results in mathematics and has no meaning the same as when divided by zero. The problem is not that you cannot be able to calculate it, but simply it doesn’t have any sense. If we place the value of \(0!\) to \(1\), we can get the expected values for \(n!\). Our factorials calculator determines the factorial of zero and other positive integers as well.

How Factorial Calculator Works:

Calculating factorial becomes handy by using this free factorial finder that allows you to:

  • Simplify simple Fatcorials
  • Add two factorials
  • Subtract two factorials
  • Multiply two factorials
  • Divide two factorials

Stick to the given steps to simplify factorials by using this calculator.

Input:

  • First, select the one option that we mentioned above to calculate factorials
  • Now, add the values according to the selected option
  • At last, make a click on the give calculate button

Output:

The factorial calculator calculates either:

  • Factorial (!) for the given number
  • Factorial of two numbers using arithmetic operations (+,-, *, /)

How to Calculate Factorial of Number (Step-by-Step):

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.

To calculate (n!):

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:

\(8! = 40320\)

Besides manual calculation, an online factorial expression calculator is the best way to express (n!) for any given whole number.

To calculate (n! + m!):

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:

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

\(n! + m! = 30\)

To calculate (n! – m!):

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:

\(n! – m! = 120 – 6\)

\(n! – m! = 114\)

To calculate (n! x m!):

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:

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

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

To calculate (n! / m!):

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 do all the calculations according to the factorial formula and determine the instant results accurately.

Frequently Ask Questions (FAQ’s):

How to calculate factorial in excel?

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

What does the symbol ! mean?

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

What is N factorial times n factorial?

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

How do I answer this one? (k+1)! + (k+1)!?

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

Final-Words:

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 determines 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.

Basic Values of Factorials:

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

 

References:

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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