**Part 1: Introduce**

**Definition**

The FACT function in Microsoft Excel calculates the factorial of a given number.

**Purpose**

The factorial of a number represents the product of all positive integers up to that number. For instance, the factorial 5 is 5 x 4 x 3 x 2 x 1. The FACT function is used to determine the number of ways a group of distinct items can be arranged (also known as permutations).

**Syntax & Arguments**

`FACT(number)`

**Explain the Arguments in the function**

**Number**: This is a required argument. It represents the nonnegative number for which you want the factorial. If the number is not an integer, it is truncated.

**Return value**

The function returns the factorial of the provided number.

**Remarks**

- The factorial of 0 is 1.
- The FACT function returns an error value if a negative number is provided.

**Part 2: Examples**

**Example 1: Factorial of 3**

**Purpose of Example**: Calculate the factorial of 3.

**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 3 `=FACT(A2)`

6 3 4 **Explanation**: The formula`=FACT(3)`

returns the factorial of 3, 3 x 2 x 1 = 6.

**Example 2: Factorial of 4**

**Purpose of Example**: Calculate the factorial of 4.

**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 4 `=FACT(A2)`

24 3 4 **Explanation**: The formula`=FACT(4)`

returns the factorial of 4, which is 4 x 3 x 2 x 1 = 24.

**Example 3: Factorial of 6**

**Purpose of Example**: Calculate the factorial of 6.

**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 6 `=FACT(A2)`

720 3 4 **Explanation**: The formula`=FACT(6)`

returns the factorial of 6, which is 6 x 5 x 4 x 3 x 2 x 1 = 720.

**Example 4: Factorial of 0**

**Purpose of Example**: Demonstrate that the factorial of 0 is 1.

**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 0 `=FACT(A2)`

1 3 4 **Explanation**: The formula`=FACT(0)`

returns the factorial of 0, which is always 1.

**Example 5: Factorial of a Decimal**

**Purpose of Example**: Calculate the factorial of the integer part of 2.5.

**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 2.5 `=FACT(A2)`

2 3 4 **Explanation**: The formula`=FACT(2.5)`

returns the factorial of the integer part 2.5, which is 2 x 1 = 2.**Example 6: FACT with IF****Purpose of Example**: Determine if a number is less than 5 and then calculate its factorial.**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 4 `=IF(A2<5, FACT(A2), "Too large")`

24 3 6 `=IF(A3<5, FACT(A3), "Too large")`

Too large 4 3 `=IF(A4<5, FACT(A4), "Too large")`

6 **Explanation**: The formula first checks if the number in column A is less than 5. If it is, it calculates the factorial of that number. If not, it returns “Too large”.

**Example 7: FACT with SUM****Purpose of Example**: Sum two numbers and then calculate the factorial of the result.**Data Sheet and Formulas**:A B C D 1 **Num1****Num2****Formula****Result**2 1 2 `=FACT(SUM(A2:B2))`

6 3 2 1 `=FACT(SUM(A3:B3))`

6 4 0 2 `=FACT(SUM(A4:B4))`

2 **Explanation**: This formula sums the numbers in columns A and B, then calculates the sum’s factorial.

**Example 8: FACT with VLOOKUP****Purpose of Example**: Use VLOOKUP to find a number in a table and then calculate the factorial of the found number.**Data Sheet and Formulas**:A B C D 1 **Key****Value****Formula****Result**2 “A” 3 `=FACT(VLOOKUP("A", A2:B4, 2, FALSE))`

6 3 “B” 2 4 “C” 4 **Explanation**: The formula uses VLOOKUP to find the key “A” in the table and retrieves its corresponding value. It then calculates the factorial of the retrieved value.

**Example 9: FACT with AVERAGE****Purpose of Example**: Calculate the factorial of the average of a range of numbers.**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 1 `=FACT(AVERAGE(A2:A4))`

2 3 2 4 3 **Explanation**: This formula calculates the average of the numbers in column A and then computes the factorial of the average.

**Example 10: FACT with MAX****Purpose of Example**: Find the maximum number in a range and then calculate the factorial of the maximum number.**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 1 `=FACT(MAX(A2:A4))`

6 3 2 4 3 **Explanation**: The formula finds the maximum number in column A and then calculates the factorial of the maximum number.

**Example 11: FACT with MIN****Purpose of Example**: Determine the minimum number in a range and then compute the factorial of the minimum number.**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 1 `=FACT(MIN(A2:A4))`

1 3 2 4 3 **Explanation**: This formula identifies the minimum number in column A and then computes the factorial of the minimum number.

**Example 12: FACT with ROUND****Purpose of Example**: Round a number to the nearest integer and then calculate the factorial of the rounded number.**Data Sheet and Formulas**:A B C 1 **Number****Formula****Result**2 2.5 `=FACT(ROUND(A2, 0))`

6 3 3.4 `=FACT(ROUND(A3, 0))`

6 4 4.6 `=FACT(ROUND(A4, 0))`

120 **Explanation**: The formula rounds the numbers in column A to the nearest integer and then calculates the factorial of the rounded number.

**Part 3: Tips and Tricks**

- Always ensure that the number provided as an argument is valid. Providing a negative number will result in an error.
- The FACT function can be combined with other functions for more complex calculations.
- Remember that the factorial of a number proliferates, so be cautious with large numbers to avoid extensive results.