# Fungrim entry: 8621f6

$\gcd\!\left(r s, c\right) = \gcd\!\left(r, c\right) \gcd\!\left(s, c\right)$
Assumptions:$r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1$
TeX:
\gcd\!\left(r s, c\right) = \gcd\!\left(r, c\right) \gcd\!\left(s, c\right)

r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("8621f6"),
Formula(Equal(GCD(Mul(r, s), c), Mul(GCD(r, c), GCD(s, c)))),
Variables(r, s, c),
Assumptions(And(Element(r, ZZ), Element(s, ZZ), Element(c, ZZ), Equal(GCD(r, s), 1))))

## 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