{
  "software": "apple-numbers",
  "function": "GCD",
  "native_application_execution": false,
  "checked_date": "2026-10-12",
  "method": "Independent mathematical/text-processing models, not Apple Numbers or Zoho Sheet execution; random tests check documented bounds/transforms, not randomness.",
  "official_function_reference": "https://support.apple.com/guide/functions/gcd-ffa58ff3ae/15.4/web/1.0",
  "passed": 9,
  "total": 9,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(48,18)",
      "variables": {},
      "expected": 6,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(14,21)",
      "variables": {},
      "expected": 7,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(24.9,36.8)",
      "variables": {},
      "expected": 12,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(15,25)",
      "variables": {},
      "expected": 5,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(64,96)",
      "variables": {},
      "expected": 32,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(99,102)",
      "variables": {},
      "expected": 3,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(17,29)",
      "variables": {},
      "expected": 1,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(99,102,105)",
      "variables": {},
      "expected": 3,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(18,30,42)",
      "variables": {},
      "expected": 6,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 203,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(48,18)",
      "actual_independent_model": 6,
      "expected": 6,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 204,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(14,21)",
      "actual_independent_model": 7,
      "expected": 7,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 205,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(24.9,36.8)",
      "actual_independent_model": 12,
      "expected": 12,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 206,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(15,25)",
      "actual_independent_model": 5,
      "expected": 5,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 207,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(64,96)",
      "actual_independent_model": 32,
      "expected": 32,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 208,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(99,102)",
      "actual_independent_model": 3,
      "expected": 3,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 209,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(17,29)",
      "actual_independent_model": 1,
      "expected": 1,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 210,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(99,102,105)",
      "actual_independent_model": 3,
      "expected": 3,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 211,
      "software": "apple-numbers",
      "function": "GCD",
      "expression": "GCD(18,30,42)",
      "actual_independent_model": 6,
      "expected": 6,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}