# Fungrim entry: 6880d0

$\gcd\!\left(a, b\right) = \max \left\{ d : d \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b \right\}$
Assumptions:$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(a \ne 0 \;\mathbin{\operatorname{or}}\; b \ne 0\right)$
TeX:
\gcd\!\left(a, b\right) = \max \left\{ d : d \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b \right\}

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(a \ne 0 \;\mathbin{\operatorname{or}}\; b \ne 0\right)
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Maximum$\mathop{\max}\limits_{x \in S} f(x)$ Maximum value of a set or function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("6880d0"),
Formula(Equal(GCD(a, b), Maximum(Set(d, For(d), And(Element(d, ZZGreaterEqual(1)), Divides(d, a), Divides(d, b)))))),
Variables(a, b),
Assumptions(And(Element(a, ZZ), Element(b, ZZ), Or(NotEqual(a, 0), NotEqual(b, 0)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC