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Factorial Calculator

Choose Factorial or an operation, enter the non-negative number, and click “Calculate” to compute n! or to add, subtract, multiply, or divide factorials.

Calculate Factorials using:

Factorial of n!

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Factorial Calculator

Our Factorial Calculator computes the factorial (n!) of any non-negative integer and provides a detailed, step-by-step breakdown. It can also perform addition, subtraction, multiplication, and division between the factorials of two different numbers.

What is a Factorial?

In mathematics, the factorial of a number n, denoted as n!, is the product of all positive integers from 1 up to n. Factorials are used to count arrangements and combinations of objects.

For example:

5! = 5 × 4 × 3 × 2 × 1 = 120
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Factorial Formula:

n! = n × (n-1) × (n-2) × … × 1

Where:

n is a non-negative integer whose factorial is being calculated.

How to Use the Factorial Calculator

Follow these simple steps:

Select an Operation: Compute a single factorial or perform arithmetic between two factorials.
Enter Numbers: Input one or two non-negative integers based on your selected operation.
Click “Calculate”: The calculator displays the final result along with step-by-step expansions.

Output Includes:

The numeric result of the factorial or operation
Expanded steps showing each multiplication
If arithmetic is performed, each factorial and the operation process is shown

Operations Supported:

Single Factorial:

Example:

5! = 5 × 4 × 3 × 2 × 1 = 120

Add Two Factorials:

Example:

5! = 120

4! = 24

5! + 4! = 120 + 24 = 144

Subtract Two Factorials:

Example:

6! = 720

5! = 120

6! - 5! = 720 - 120 = 600

Multiply Two Factorials:

Example:

4! = 24

3! = 6

4! × 3! = 24 × 6 = 144

Divide Two Factorials:

Example:

6! = 720

4! = 24

6! ÷ 4! = 720 ÷ 24 = 30

Why Factorials Are Undefined for Negative Numbers

Factorials are only defined for non-negative integers. Negative numbers do not represent a valid number of arrangements, so factorials of negative numbers are undefined. Our calculator only accepts inputs where n ≥ 0.

Factorial of 0 (0!)

Special Case:

0! is defined as 1. This is supported by combinatorics and recursive definitions.

Combinatorial Explanation:

0! counts the ways to arrange zero objects, which is exactly 1 way.

Recursive Explanation:

Factorials follow n! = n × (n-1)!. To keep this consistent, 0! is defined as 1.

Step-by-Step Examples

Single Factorial:

Example: 8!

Step 1: 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Step 2: 8! = 40320

Add Factorials:

Example: 3! + 4!

3! = 6

4! = 24

3! + 4! = 6 + 24 = 30

Subtract Factorials:

Example: 5! - 3!

5! = 120

3! = 6

5! - 3! = 114

Multiply Factorials:

Example: 7! × 4!

7! = 5040

4! = 24

7! × 4! = 120960

Divide Factorials:

Example: 5! ÷ 6!

5! = 120

6! = 720

5! ÷ 6! = 0.1667

Frequently Asked Questions

What does n! mean?

n! is the product of n and all positive integers below it down to 1.

Where are factorials used?

Factorials appear in permutations, combinations, probability, series expansions, calculus, and many mathematical formulas.

How to calculate factorial in Excel?

Use the function =FACT(n) to compute the factorial of n.

What is n! × n!?

Multiplying a factorial by itself yields (n!)². For example, 3! × 3! = 36.

Common Factorial Values

n!	Value
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!	1.19622E+56
50!	3.04141E+64
100!	9.33262E+157

Conclusion

Factorials are a fundamental concept in mathematics, particularly in counting, probability, and calculus. A factorial calculator simplifies computation and allows arithmetic between factorials quickly. For deeper number exploration, consider prime factor calculators to examine factorization and divisibility properties.

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