Category:Examples of Greatest Common Divisors
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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 $\gcd \set {a, b}$.
When $a = b = 0$, $\gcd \set {a, b}$ is undefined.
Subcategories
This category has only the following subcategory.
Pages in category "Examples of Greatest Common Divisors"
The following 11 pages are in this category, out of 11 total.
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- Greatest Common Divisor of Integers/Examples
- Greatest Common Divisor of Integers/Examples/-12 and 30
- Greatest Common Divisor of Integers/Examples/-5 and 5
- Greatest Common Divisor of Integers/Examples/-8 and -36
- Greatest Common Divisor of Integers/Examples/12 and -8
- Greatest Common Divisor of Integers/Examples/20, 70 and 80
- Greatest Common Divisor of Integers/Examples/8 and 17
- Greatest Common Divisor of Integers/Examples/n and 0
- Greatest Common Divisor of Set of Integers/Examples
- Greatest Common Divisor of Set of Integers/Examples/39, 42, 54
- Greatest Common Divisor of Set of Integers/Examples/49, 210, 350