The FACT formula with example in Excel

The FACT function in Excel is used to calculate the factorial of a given number. The factorial of a number $𝑛$ (denoted as $𝑛!$) is the product of all positive integers from 1 to $𝑛$. It is commonly used in permutations, combinations, and other areas of mathematics and statistics.

Syntax

excel
FACT(number)

• number: The non-negative integer for which you want to calculate the factorial.

Examples

Let's look at some examples to understand how the FACT function works.

Example 1: Basic Usage

Suppose you want to calculate the factorial of 5.

1. In cell A1, enter the number:

   excel
   5
   

2. In cell B1, enter the formula:

   excel
   =FACT(A1)
   

   This will output 120, because $5!=5\times 4\times 3\times 2\times 1=120$.

Example 2: Factorial of Zero

The factorial of 0 is defined as 1.

1. In cell A2, enter the number:

   excel
   0
   

2. In cell B2, enter the formula:

   excel
   =FACT(A2)
   

   This will output 1, because $0!=1$.

Example 3: Factorial of a Larger Number

Suppose you want to calculate the factorial of 7.

1. In cell A3, enter the number:

   excel
   7
   

2. In cell B3, enter the formula:

   excel
   =FACT(A3)
   

   This will output 5040, because $7!=7\times 6\times 5\times 4\times 3\times 2\times 1=5040$.

Practical Use Cases

1. Combinatorics: Calculating permutations and combinations, such as determining the number of ways to arrange a set of items.
2. Probability: Used in probability theory to calculate the likelihood of events.
3. Mathematical Problems: Solving various mathematical problems that involve factorial calculations.

Example: Combinations Calculation

Suppose you want to calculate the number of ways to choose 3 items from a set of 5 (denoted as $\left(\genfrac{}{}{0px}{}{5}{3}\right)$). The formula for combinations is:

$\left(\genfrac{}{}{0px}{}{𝑛}{𝑘}\right)=\frac{𝑛!}{𝑘!(𝑛-𝑘)!}$

You can use the FACT function to calculate this in Excel.

1. In cell A4, enter the total number of items (n):

   excel
   5
   

2. In cell B4, enter the number of items to choose (k):

   excel
   3
   

3. In cell C4, enter the formula to calculate the combination:

   excel
   =FACT(A4) / (FACT(B4) * FACT(A4 - B4))
   

   This will output 10, because $\left(\genfrac{}{}{0px}{}{5}{3}\right)=\frac{5!}{3!\times 2!}=\frac{120}{6\times 2}=10$.

Notes

• Non-negative Integers: The FACT function only works with non-negative integers. If you input a negative number or a non-integer, Excel will return a #NUM! error.
• Large Numbers: Factorials grow very quickly with larger numbers, so the results can become extremely large.

Summary

The FACT function in Excel is a useful tool for calculating the factorial of a number, which has applications in combinatorics, probability, and various mathematical problems. By understanding how to use the FACT function, you can efficiently perform complex calculations involving factorials in your Excel worksheets.