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  "body": "\n## Definition\n\nLet $a$ and $b$ be integers that are not both $0$.\nA common divisor of $a$ and $b$ is an integer $d$ such that $d \\mid a$ and $d \\mid b$.\nThe greatest common divisor $\\gcd(a, b)$ is the largest common divisor of $a$ and $b$.\nBy convention, $\\gcd(0, 0) = 0$.\n\n## Remarks\n\nThe number $\\gcd(a, b)$ is positive when $a$ and $b$ are not both $0$, because $1$ is a common divisor.\nAn equivalent definition: $\\gcd(a, b)$ is the unique nonnegative common divisor of $a$ and $b$ that each common divisor [[divides|096PW7Q014]]. This form also gives $\\gcd(0, 0) = 0$.\nFor all integers $a$, $\\gcd(a, 0) = |a|$.\nThe [[Euclidean algorithm|0TRNT4X7J0]] computes $\\gcd(a, b)$.\n\n## Explanations\n\n### L1 human\n\nList the positive divisors of each number, and take the largest number that is in both lists.\nThe divisors of $12$ are $1, 2, 3, 4, 6, 12$, and the divisors of $18$ are $1, 2, 3, 6, 9, 18$.\nThus $\\gcd(12, 18) = 6$.\n",
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