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  "body": "\n## Summary\n\nA GCD domain is an [[integral domain|09S3PFBEPM]] in which any two elements have a [[greatest common divisor|0F7KNJ1ZYN]].\nEvery [[unique factorisation domain|06YMXJMXYS]] and every [[Bézout domain|HGEX40P0Z0]] is a GCD domain.\nIn a GCD domain every [[irreducible element|052SDEPZH7]] is [[prime|0MNHXBSX3M]], and the ring is [[integrally closed|H20P600HQS]].\nGCD domains need not have factorizations into irreducibles, so the notion is strictly weaker than unique factorization.\n\n## Explanations\n\n### L1 human\n\nIn the integers, any two numbers have a greatest common divisor, such as $\\gcd(12, 18) = 6$.\nA GCD domain is a ring where this keeps working: among the common divisors of $a$ and $b$ there is one that every other common divisor divides.\nThe ring $\\Z[\\sqrt{-5}]$ is not a GCD domain: the elements $6$ and $2(1 + \\sqrt{-5})$ have the common divisors $2$ and $1 + \\sqrt{-5}$, but no common divisor is divisible by both.\n",
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