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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.