# GCD Function in Excel

GCD Function in Microsoft Excel

### Part 1: Introduce

Definition:
The GCD function in Microsoft Excel returns the greatest common divisor of two or more integers.

Purpose:
To determine the largest integer that divides the given numbers without leaving a remainder.

Syntax & Arguments:

syntax
`GCD(number1, [number2], ...) `

Explain the Arguments in the function:

• Number1, number2, …: Number1 is mandatory, while subsequent numbers are optional. You can provide between 1 to 255 values. If any matter is not an integer, it will be truncated.

Return value:
The GCD function will return the greatest common divisor of the provided integers.

Remarks:

1. If any argument is nonnumeric, GCD returns the `#VALUE!` error value.
2. If any argument is opposing, GCD returns the `#NUM!` error value.
3. The number one divides any value evenly.
4. A prime number only has itself and one as even divisors.
5. If a parameter to GCD is greater than or equal to 2^53, GCD returns the `#NUM!` error value.

### Part 2: Examples

Example 1:

• Purpose of illustration: To find the greatest common divisor of 8 and 12.
• Data sheet and formulas:
ABCD
1Data1Data2FormulaResult
2812`=GCD(A2,B2)`4
• Explanation: The greatest common divisor of 8 and 12 is 4.

Example 2:

• Purpose of illustration: To find the greatest common divisor of 15, 25, and 35.
• Data sheet and formulas:
ABCDE
1Data1Data2Data3FormulaResult
2152535`=GCD(A2,C2)`5
• Explanation: The greatest common divisor of 15, 25, and 35 is 5.

Example 3:

• Purpose of illustration: To find the greatest common divisor of 7 and 49.
• Data sheet and formulas:
ABCD
1Data1Data2FormulaResult
2749`=GCD(A2,B2)`7
• Explanation: The greatest common divisor of 7 and 49 is 7, as 7 is a factor of both numbers.

Example 4:

• Purpose of illustration: To find the greatest common divisor of 9 and 15.
• Data sheet and formulas:
ABCD
1Data1Data2FormulaResult
2915`=GCD(A2,B2)`3
• Explanation: The greatest common divisor of 9 and 15 is 3.

Example 5:

• Purpose of illustration: To find the greatest common divisor of 21, 28, and 35.
• Data sheet and formulas:
ABCDE
1Data1Data2Data3FormulaResult
2212835`=GCD(A2,C2)`7
• Explanation: The greatest common divisor of 21, 28, and 35 is 7.

Example 6: Using GCD with IF Function

• Purpose of example: Find the GCD of two numbers if their sum exceeds 50; otherwise, return “Too Small”.
• Data sheet and formulas:
ABCD
1Data1Data2FormulaResult
23520`=IF(SUM(A2,B2)>50, GCD(A2,B2), "Too Small")`5
• Explanation: Since the sum of 35 and 20 is 55, greater than 50, the GCD of 35 and 20 is calculated, which is 5.

Example 7: Using GCD with SUM Function

• Purpose of example: To find the GCD of the sum of three numbers and another number.
• Data sheet and formulas:
ABCDE
1Data1Data2Data3FormulaResult
2121518`=GCD(SUM(A2:C2), 45)`15
• Explanation: The sum of 12, 15, and 18 is 45. The GCD of 45 and 45 is 15.

Example 8: Using GCD with VLOOKUP Function

• Purpose of example: To find the GCD of a value in a table using VLOOKUP and another given number.
• Data sheet and formulas:
ABCD
1KeyValueFormulaResult
2124`=GCD(VLOOKUP(1, A2:B2, 2, FALSE), 36)`12
• Explanation: The VLOOKUP function finds the value corresponding to the key 1, which is 24. The GCD of 24 and 36 is 12.

Example 9: Using GCD with AVERAGE Function

• Purpose of example: To find the GCD of the average of three numbers and another number.
• Data sheet and formulas:
ABCDE
1Data1Data2Data3FormulaResult
2102030`=GCD(AVERAGE(A2:C2), 25)`5
• Explanation: The average of 10, 20, and 30 is 20. The GCD of 20 and 25 is 5.

Example 10: Using GCD with MAX Function

• Purpose of example: To find the GCD of the maximum value among three numbers and another number.
• Data sheet and formulas:
ABCDE
1Data1Data2Data3FormulaResult
2142842`=GCD(MAX(A2:C2), 56)`14
• Explanation: The maximum value among 14, 28, and 42 is 42. The GCD of 42 and 56 is 14.

Example 11: Using GCD with MIN Function

• Purpose of example: To find the GCD of the minimum value among three numbers and another number.
• Data sheet and formulas:
ABCDE
1Data1Data2Data3FormulaResult
2223344`=GCD(MIN(A2:C2), 55)`11
• Explanation: The minimum value among 22, 33, and 44 is 22. The GCD of 22 and 55 is 11.

Example 12: Using GCD with CONCATENATE Function

• Purpose of illustration: To concatenate a string with the GCD of two numbers.
• Data sheet and formulas:
ABCD
1Data1Data2FormulaResult
24050`=CONCATENATE("GCD Value: ", GCD(A2,B2))`GCD Value: 10
• Explanation: The GCD of 40 and 50 is 10. The CONCATENATE function then combines this value with the “GCD Value: “string, resulting in the final text “GCD Value: 10”.

### Part 3: Tips and tricks

1. Always ensure that the numbers provided are integers. If not, the GCD function will truncate the numbers.
2. Use the GCD function to find the highest common factor of two or more numbers.
3. Be cautious when providing large numbers as arguments, as values greater than or equal to 2^53 will result in an error.
4. The GCD function can be especially useful in mathematical and algebraic calculations where determining common factors is essential.