# FACT Function in Excel

### 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

syntax
```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.

### Example 1: Factorial of 3

Purpose of Example: Calculate the factorial of 3.

• Data Sheet and Formulas:

ABC
1NumberFormulaResult
23`=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:

ABC
1NumberFormulaResult
24`=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:

ABC
1NumberFormulaResult
26`=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:

ABC
1NumberFormulaResult
20`=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:

ABC
1NumberFormulaResult
22.5`=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:

ABC
1NumberFormulaResult
24`=IF(A2<5, FACT(A2), "Too large")`24
36`=IF(A3<5, FACT(A3), "Too large")`Too large
43`=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:

ABCD
1Num1Num2FormulaResult
212`=FACT(SUM(A2:B2))`6
321`=FACT(SUM(A3:B3))`6
402`=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:

ABCD
1KeyValueFormulaResult
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:

ABC
1NumberFormulaResult
21`=FACT(AVERAGE(A2:A4))`2
32
43
• 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:

ABC
1NumberFormulaResult
21`=FACT(MAX(A2:A4))`6
32
43
• 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:

ABC
1NumberFormulaResult
21`=FACT(MIN(A2:A4))`1
32
43
• 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:

ABC
1NumberFormulaResult
22.5`=FACT(ROUND(A2, 0))`6
33.4`=FACT(ROUND(A3, 0))`6
44.6`=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.