Coprime integers

Definition

Two integers $a$ and $b$ are coprime when their greatest common divisor is $1$, that is, when $\gcd(a, b) = 1$.

Remarks

Equivalently, $a$ and $b$ are coprime when the only integers that divide both of them are $1$ and $-1$. For example, $8$ and $15$ are coprime, but $8$ and $12$ are not, because $4$ divides both. The integers $1$ and $-1$ are coprime to each integer. The integer $0$ is coprime only to $1$ and $-1$. By Bézout's identity, $a$ and $b$ are coprime if and only if $a x + b y = 1$ for some integers $x$ and $y$.

Explanations

L1 human

Two numbers are coprime when they have no common factor except $1$. The numbers do not need to be prime themselves: $9$ and $10$ are not prime, but they are coprime. A fraction $a / b$ is in lowest terms exactly when $a$ and $b$ are coprime.