Factorial Calculator

Category: Algebra II
- May 14, 2025
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Calculate the factorial of a number. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

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About Factorials

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n.

Properties of Factorials
  • Definition: n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
  • Base Case: 0! = 1 (by definition)
  • Growth Rate: Factorials grow extremely quickly. 10! is already over 3.6 million.
  • Recurrence Relation: n! = n × (n-1)!
Applications of Factorials

Factorials are used in various mathematical and real-world applications:

  • Combinatorics and permutations
  • Probability theory
  • Taylor series expansions
  • Statistical distributions
  • Number theory

Factorial Formula: n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1

Special Case: 0! = 1

What Is the Factorial Calculator?

The Factorial Calculator is a simple tool that calculates the factorial of a non-negative integer. A factorial, written as n!, is the product of all positive integers less than or equal to n. It is widely used in combinatorics, probability, algebra, and various real-world problem-solving scenarios.

This calculator ensures fast and accurate results, allowing users to customize the number of decimal places, view scientific notation, and even see detailed calculation steps if needed.

How to Use the Factorial Calculator

  • Enter a whole number between 0 and 170 into the input field labeled "Number (0-170)".
  • Choose the number of decimal places you want to display in the result from the dropdown menu.
  • Optionally, select checkboxes to show calculation steps or display the result in scientific notation.
  • Click the "Calculate" button to see the result.
  • Use the "Reset" button to clear your inputs and start again.

Why Use a Factorial Calculator?

Calculating factorials by hand can become tedious and prone to mistakes, especially for larger numbers. This tool offers:

  • Instant, accurate results for numbers up to 170.
  • Display options for easier reading and understanding.
  • Step-by-step breakdowns for educational purposes.
  • Scientific notation for handling extremely large values effectively.

Whether you are studying mathematical concepts, preparing for exams, or solving real-world problems, this calculator can save you time and improve accuracy.

Practical Applications of Factorials

  • Combinatorics: Determining the number of ways to arrange or select items.
  • Probability: Calculating chances and outcomes.
  • Series Expansions: Using factorials in Taylor and Maclaurin series.
  • Algebra and Number Theory: Solving advanced mathematical problems.

Related Tools You Might Find Useful

If you are interested in solving more complex problems, you might also explore tools like:

  • Inverse Function Calculator: Easily find inverse functions and solve for inverses using the inverse function tool or inverse equation solver.
  • Logarithm Calculator: Use the base log finder and logarithm equation helper to solve logarithmic functions and calculate logarithms effectively.
  • Midpoint Calculator: Quickly find the midpoint between two points with the coordinate midpoint finder or midpoint formula tool.
  • Complex Number Calculator: Handle complex number operations, including adding and multiplying complex numbers, and converting between polar and rectangular forms.
  • Operations on Functions Calculator: Combine functions easily by adding, subtracting, multiplying, or dividing functions.

Frequently Asked Questions (FAQ)

What is a factorial?

A factorial, represented by an exclamation mark (n!), is the product of all positive integers up to a given number n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Why does the calculator limit inputs to 170?

Numbers larger than 170! exceed the capacity of JavaScript’s number system to handle accurately, leading to unreliable results. Therefore, the calculator restricts inputs to a safe range.

Can I see how the factorial is calculated?

Yes! Simply check the "Show calculation steps" box to view a breakdown of how the factorial is computed step-by-step.

What if I need scientific notation?

The calculator can display results in scientific notation if you select the "Show scientific notation" option, making very large numbers easier to read.

Is there a special value for 0!?

Yes, by definition, the factorial of 0 is 1.

What are some related topics?

After mastering factorials, you might explore topics like finding polynomial roots using a Polynomial Roots Calculator, solving partial fractions with a Partial Fraction Decomposition Calculator, or learning about inverse trigonometric functions with the Inverse Sine Calculator and Inverse Tangent Calculator.