# A to Z of Excel Functions: the GCD Function

10 February 2020

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the GCD function. *

**The GCD function**

In mathematics, the greatest common divisor (GCD), also known as the greatest common denominator or the highest common factor, of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 180 and 48 is 12.

To show this, if we factorise the numbers down to primes:

180 = 2 x 2 x 3 x 3 x 5

48 = 2 x 2 x 2 x 2 x 3

Therefore, the prime numbers shared are:

2 x 2 x 3 = 12.

A much more efficient method is the Euclidean algorithm, which uses the division algorithm in combination with the observation that the GCD of two numbers also divides their difference:

- Divide 180 by 48 is 3 remainder 36, so
- Divide 48 by 36 is 1 remainder 12, so
- Divide 36 by 12 is 3 with no remainder.

Therefore, 12 is the GCD of 180 and 48.

The Excel function **GCD **returns the greatest common divisor of two or more integers. The greatest common divisor is the largest integer that divides both **number1** and **number2** without a remainder. It has the following syntax:

**GCD(number1, [number2], ...)**

The **GCD** function has the following arguments:

**number1**,**number2**, ... where**number1**is required, and subsequent numbers are optional. There can be between one (1) and 255 numbers. If any value is not an integer, it is truncated.

It should be further noted that:

- if any argument is nonnumeric,
**GCD**returns the*#VALUE!*error value - if any argument is less than zero,
**GCD**returns the*#NUM!*error value - one divides any value evenly
- a prime number has only itself and one as divisors
- if a parameter to
**GCD**is >=2^53,**GCD**returns the*#NUM!*error value.

Please see my example below:

*We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every business day.*

*A full page of the function articles can be found here. *