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`	$\gcd\!\left(n, k\right)$	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

Greatest common divisor