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  "body": "\n## Definition\n\nTwo integers $a$ and $b$ are coprime when their [[greatest common divisor|02WF878BH1]] is $1$, that is, when $\\gcd(a, b) = 1$.\n\n## Remarks\n\nEquivalently, $a$ and $b$ are coprime when the only integers that divide both of them are $1$ and $-1$.\nFor example, $8$ and $15$ are coprime, but $8$ and $12$ are not, because $4$ divides both.\nThe integers $1$ and $-1$ are coprime to each integer. The integer $0$ is coprime only to $1$ and $-1$.\nBy [[Bézout's identity|0DQVHMYAGA]], $a$ and $b$ are coprime if and only if $a x + b y = 1$ for some integers $x$ and $y$.\n\n## Explanations\n\n### L1 human\n\nTwo numbers are coprime when they have no common factor except $1$.\nThe numbers do not need to be prime themselves: $9$ and $10$ are not prime, but they are coprime.\nA fraction $a / b$ is in lowest terms exactly when $a$ and $b$ are coprime.\n",
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