# Fungrim entry: 646745

$\gcd\!\left(\frac{a}{d}, \frac{b}{d}\right) = \frac{\gcd\!\left(a, b\right)}{\left|d\right|}$
Assumptions:$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b$
TeX:
\gcd\!\left(\frac{a}{d}, \frac{b}{d}\right) = \frac{\gcd\!\left(a, b\right)}{\left|d\right|}

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Abs$\left|z\right|$ Absolute value
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("646745"),
Formula(Equal(GCD(Div(a, d), Div(b, d)), Div(GCD(a, b), Abs(d)))),
Variables(a, b, d),
Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(d, ZZ), Divides(d, a), Divides(d, b))))

## 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