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Factorial Expression Calculator

Factorial Expression:

\[ \frac{n!}{m!} \text{ or other factorial expressions} \]

integer
integer

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1. What is a Factorial Expression?

A factorial expression involves operations with factorials, denoted by the exclamation mark (!). The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. This calculator handles common factorial operations like division, multiplication, addition, and subtraction.

2. How Does the Calculator Work?

The calculator computes factorial expressions using the formula:

\[ \text{Selected operation between } n! \text{ and } m! \]

Where:

Note: 0! is defined as 1 by convention.

3. Understanding Factorials

Details: Factorials grow very rapidly with increasing n. The calculator limits input to 170 because 171! exceeds PHP's float maximum value. Factorials are fundamental in combinatorics, probability, and many areas of mathematics.

4. Using the Calculator

Tips: Enter non-negative integers for n and m (0-170), select an operation, and click Calculate. Results are displayed in both exact and decimal forms when applicable.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a limit of 170?
A: Factorials grow extremely fast. 171! ≈ 1.24×10³⁰⁹ which exceeds maximum floating-point number representations in most programming languages.

Q2: What is 0! ?
A: 0! is defined as 1, which is important for many mathematical formulas to work correctly in edge cases.

Q3: Can I calculate factorials of non-integers?
A: This calculator only handles non-negative integers. For non-integers, you would need the gamma function (Γ(n) = (n-1)!).

Q4: Why are factorial operations important?
A: Factorial expressions are crucial in combinatorics (counting permutations and combinations), probability, series expansions, and many other mathematical areas.

Q5: How accurate are the results?
A: Results are exact for integer operations up to 170, though displayed in decimal form for division results. For very large numbers, floating-point precision limitations may apply.

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