# Category:Examples of Greatest Common Divisors

This category contains examples of Greatest Common Divisor of Integers.

Let $a, b \in \Z: a \ne 0 \lor b \ne 0$.

### Definition 1

The greatest common divisor of $a$ and $b$ is defined as:

the largest $d \in \Z_{>0}$ such that $d \divides a$ and $d \divides b$

### Definition 2

The greatest common divisor of $a$ and $b$ is defined as the (strictly) positive integer $d \in \Z_{>0}$ such that:

$(1): \quad d \divides a \land d \divides b$
$(2): \quad c \divides a \land c \divides b \implies c \divides d$

This is denoted $\gcd \set {a, b}$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Examples of Greatest Common Divisors"

The following 7 pages are in this category, out of 7 total.