Category:Greatest Common Divisor
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This category contains results about Greatest Common Divisor.
Definitions specific to this category can be found in Definitions/Greatest Common Divisor.
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 the following 7 subcategories, out of 7 total.
B
E
G
L
P
Pages in category "Greatest Common Divisor"
The following 42 pages are in this category, out of 42 total.
B
E
G
- GCD and LCM Distribute Over Each Other
- GCD and LCM from Prime Decomposition
- GCD for Negative Integers
- GCD from Congruence Modulo m
- GCD from Generator of Ideal
- GCD from Prime Decomposition
- GCD from Prime Decomposition/General Result
- GCD of Consecutive Integers of General Fibonacci Sequence
- GCD of Fibonacci Numbers
- GCD of Generators of General Fibonacci Sequence is Divisor of All Terms
- GCD of Integer and Divisor
- GCD of Integer and its Negative
- GCD of Polynomials does not depend on Base Field
- GCD of Sum and Difference of Integers
- GCD with One Fixed Argument is Multiplicative Function
- GCD with Prime
- GCD with Remainder
- GCD with Zero
- Greatest Common Divisor divides Lowest Common Multiple
- Greatest Common Divisor in Principal Ideal Domain is Expressible as Linear Combination
- Greatest Common Divisor is Associative
- Greatest Common Divisor is at least 1
- Greatest Common Divisors in Principal Ideal Domain are Associates