Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 is 4.

The greatest common divisor is also known as the greatest common factor (gcf),highest common factor (hcf),greatest common measure (gcm), or highest common divisor.

This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below).

In this article we will denote the greatest common divisor of two integers a and b as gcd(a,b). Some textbooks use (a,b).

What is the greatest common divisor of 54 and 24?

The number 54 can be expressed as a product of two integers in several different ways:

Thus the divisors of 54 are: ${\displaystyle 1,2,3,6,9,18,27,54.\,}$

Similarly, the divisors of 24 are: ${\displaystyle 1,2,3,4,6,8,12,24.\,}$

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