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How to Put Factorial in Calculator Ti-84

Reviewed by Calculator Editorial Team

Calculating factorials on your TI-84 calculator is straightforward once you know the correct method. This guide will walk you through the process step-by-step, including how to input factorials in equations and programs.

Introduction

The factorial function, denoted by an exclamation mark (!), is a fundamental concept in mathematics that represents the product of all positive integers up to a given number. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

While the TI-84 doesn't have a dedicated factorial button, you can calculate factorials using the calculator's built-in functions. This guide will show you exactly how to do it.

Factorial Basics

The factorial of a non-negative integer n is defined as:

n! = n × (n-1) × (n-2) × ... × 1

0! = 1 (by definition)

Factorials are used in combinatorics, probability, algebra, and many other mathematical fields. They appear in formulas for permutations, combinations, binomial coefficients, and more.

TI-84 Factorial Method

Since the TI-84 doesn't have a direct factorial key, you'll need to use one of these methods:

  1. Use the math print (MATH) menu and select "math" → "factorial"
  2. Use the gamma function (MATH → "prob" → "gamma") with n+1
  3. Write a program to calculate factorials

The first method is the simplest for one-time calculations, while the program method is best for repeated use.

Step-by-Step Guide

Method 1: Using the Math Menu

  1. Press the MATH key
  2. Scroll down to PRB (probability) and press ENTER
  3. Scroll to ! (factorial) and press ENTER
  4. Enter the number you want to calculate the factorial of
  5. Press ENTER to see the result

Method 2: Using the Gamma Function

  1. Press the MATH key
  2. Scroll down to PRB and press ENTER
  3. Scroll to gamma( and press ENTER
  4. Enter the number you want to calculate the factorial of plus 1 (e.g., for 5!, enter 6)
  5. Press ENTER to see the result

Note: The gamma function is more general than factorial, but for integer values, gamma(n+1) = n!

Method 3: Creating a Factorial Program

For repeated use, create a program:

  1. Press PRGM → EDIT
  2. Press NEW and name it (e.g., FACT)
  3. Enter these lines:
    • Lbl FACT
    • If A=0
    • Then
    • 1→B
    • Else
    • A×fact(A-1)→B
    • End
    • Return
  4. Press EXIT to save
  5. To use: Press PRGM → EXECUTE → select FACT
  6. Enter a number and press ENTER

Examples

Let's calculate 4! using each method:

Method 1 Example

  1. MATH → PRB → !
  2. Enter 4 → ENTER
  3. Result: 24

Method 2 Example

  1. MATH → PRB → gamma(
  2. Enter 5 → ENTER
  3. Result: 24

Program Example

  1. PRGM → EXECUTE → FACT
  2. Enter 4 → ENTER
  3. Result: 24

All methods should give you the same result of 24 for 4!.

FAQ

Can I calculate factorials with decimals on the TI-84?
No, the factorial function only works with non-negative integers. For decimal values, you would need to use the gamma function.
What's the maximum number I can calculate a factorial for on the TI-84?
The TI-84 can calculate factorials up to 69! before encountering overflow errors. For larger numbers, you might need a more advanced calculator.
Is there a difference between ! and gamma( for factorials?
For integer values, gamma(n+1) equals n!. The gamma function is more general and works with non-integers, but for factorial calculations, the ! function is more straightforward.
Can I use factorials in equations on the TI-84?
Yes, you can use the factorial function in equations by using the MATH → PRB → ! method. Just enter the equation and use the factorial function where needed.