# What is 8 factorial ?

Steps to calculate factorial of 8

To find 8 factorial, or 8!, simply use the formula that multiplies the number 8 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 8:

## Factorials of Numbers similar to 8

## What is Factorial?

In mathematics, a factorial is a function applied to natural numbers that results in the product of an integer and all the positive integers that come before it. The factorial of 8 is significant because it not only represents a simple multiplication of numbers from 1 to 8 but also has numerous applications that are fundamental to various mathematical concepts, including combinatorics, probability, and sequence operations.

## Formula to Calculate the Factorial of 8

The formula for calculating a factorial is relatively straightforward:

**n! = n × (n-1) × … × 1**

For the factorial of 8, you would calculate:

**8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1**

By following these steps, you end up with:

**8! = 40320**

## What is the Factorial of 8 Used For?

The factorial of 8 has several applications in different fields:

**Combinatorics:**Used in counting permutations where order matters. For instance, the number of different ways to arrange 8 distinct books on a shelf is calculated as 8!.**Probability Theory:**In calculating probabilities where ordering is integral to the outcome of an event.**Algebra:**The factorial function appears in equations and identities, including the famous*Binomial Theorem.*

## Exercises

Test your understanding of factorials with these simple problems:

- If a code has 8 distinct symbols, how many different 8-symbol codes can you create?
- There are 8 runners in a race. How many different ways can the runners finish first, second, and third?

## Solutions to Exercises

Here are the solutions:

- The total number of different 8-symbol codes is the factorial of 8, which is 8! = 40320.
- For the runners, the problem is a permutation of 8 items taken 3 at a time. This gives us 8P3 = 8! / (8-3)! = 8 × 7 × 6 = 336 different ways.

## Frequently Asked Questions

### Q: Is 8 factorial used in computing software algorithms?

A: Yes, the concept of factorials, including 8!, is frequently used in algorithms that involve permutations and combinations, which are foundational to computer science problems and optimization challenges.

### Q: Can the factorial function be applied to non-integer numbers?

A: No, the factorial function is traditionally defined for non-negative integers only. However, the gamma function extends the concept to non-integer and complex numbers, except for negative integers.

## Other conversions of the number 8

8 in Roman numerals

8 in Spanich

8 in Italian