{
  "$schema": "https://raw.githubusercontent.com/ards-project/ard-spec/main/spec/schemas/ai-catalog.schema.json",
  "specVersion": "1.0",
  "host": {
    "displayName": "FactorCalculators",
    "identifier": "did:web:factorcalculators.com",
    "documentationUrl": "https://factorcalculators.com/about-us",
    "description": "Comprehensive mathematical computational platform specializing in integer factorization, prime decomposition, polynomial factoring, and number theory calculators."
  },
  "entries": [
    {
      "identifier": "urn:air:factorcalculators.com:tool:factor-calculator",
      "displayName": "Factor Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/factor",
      "description": "Computes all positive and negative factors of an integer, total divisor count, divisor sum, factor pairs, and checks if the number is prime, composite, or square.",
      "tags": ["factors", "divisors", "math", "integers", "arithmetic", "factor-pairs"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "number": {
            "type": "integer",
            "description": "The integer number to factorize (e.g. 36, 100, 1024)",
            "minimum": 1
          }
        },
        "required": ["number"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:prime-factor-calculator",
      "displayName": "Prime Factorization Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/prime-factor",
      "description": "Decomposes any positive integer into its canonical prime factor representation, visual factor tree, and exponential prime power form.",
      "tags": ["prime-factors", "prime-factorization", "factor-tree", "number-theory"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "number": {
            "type": "integer",
            "description": "The positive integer to decompose into prime factors",
            "minimum": 2
          }
        },
        "required": ["number"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:gcf-lcm-calculator",
      "displayName": "GCF & LCM Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/gcf-lcm",
      "description": "Calculates Greatest Common Factor (GCF/GCD) and Least Common Multiple (LCM) of two or more numbers using the Euclidean algorithm and prime power Venn methods.",
      "tags": ["gcf", "lcm", "greatest-common-factor", "least-common-multiple", "euclidean-algorithm"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "firstNumber": {
            "type": "integer",
            "description": "First integer"
          },
          "secondNumber": {
            "type": "integer",
            "description": "Second integer"
          }
        },
        "required": ["firstNumber", "secondNumber"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:factor-pairs-calculator",
      "displayName": "Factor Pairs Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/factor-pairs",
      "description": "Generates all pairs of positive and negative integers whose product equals the target number, complete with product verification.",
      "tags": ["factor-pairs", "multiplication-pairs", "divisors"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "number": {
            "type": "integer",
            "description": "The target integer"
          }
        },
        "required": ["number"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:polynomial-factoring-calculator",
      "displayName": "Polynomial Factoring Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/polynomial",
      "description": "Factors algebraic polynomials across degrees 2 to 6 by finding GCF, applying grouping, evaluating rational root candidates, and executing synthetic division.",
      "tags": ["polynomials", "algebra", "factoring", "rational-root-theorem", "synthetic-division"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "expression": {
            "type": "string",
            "description": "Algebraic polynomial expression (e.g. 'x^3 - 6x^2 + 11x - 6' or '2x^2 + 7x + 3')"
          }
        },
        "required": ["expression"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:trinomial-factoring-calculator",
      "displayName": "Trinomial Factoring Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/trinomial",
      "description": "Specialized quadratic trinomial solver factoring expressions of form ax^2 + bx + c using the AC method and splitting the linear middle term.",
      "tags": ["trinomial", "ac-method", "quadratic", "algebra"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "a": { "type": "number", "description": "Coefficient of x^2" },
          "b": { "type": "number", "description": "Coefficient of x" },
          "c": { "type": "number", "description": "Constant term" }
        },
        "required": ["a", "b", "c"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:quadratic-factoring-calculator",
      "displayName": "Quadratic Equation & Factoring Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/quadratic",
      "description": "Solves quadratic equations ax^2 + bx + c = 0 with complete step-by-step methods: factoring, quadratic formula, discriminant analysis, and vertex calculation.",
      "tags": ["quadratic", "quadratic-formula", "discriminant", "vertex", "algebra"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "a": { "type": "number", "description": "Coefficient of x^2" },
          "b": { "type": "number", "description": "Coefficient of x" },
          "c": { "type": "number", "description": "Constant term" }
        },
        "required": ["a", "b", "c"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:binomial-factoring-calculator",
      "displayName": "Binomial Factoring Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/binomial",
      "description": "Identifies and factors algebraic binomials, including difference of squares (a^2 - b^2), difference of cubes (a^3 - b^3), and sum of cubes (a^3 + b^3).",
      "tags": ["binomial", "difference-of-squares", "difference-of-cubes", "sum-of-cubes"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "expression": { "type": "string", "description": "Binomial expression (e.g. 'x^2 - 16' or '8x^3 + 27')" }
        },
        "required": ["expression"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:scale-factor-calculator",
      "displayName": "Scale Factor Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/scale-factor",
      "description": "Calculates linear scale factor dilation ratios, area scale factors (k^2), and volume scale factors (k^3) between original and scaled geometric dimensions.",
      "tags": ["scale-factor", "geometry", "dilation", "ratio", "scaling"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "originalDimension": { "type": "number", "description": "Original length or measure" },
          "scaledDimension": { "type": "number", "description": "New or scaled length or measure" }
        },
        "required": ["originalDimension", "scaledDimension"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:divisibility-rules-engine",
      "displayName": "Divisibility Rules & Test Engine",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/divisibility",
      "description": "Tests any integer against modular divisibility rules for numbers 2 through 19, returning true/false results with full mathematical reasoning.",
      "tags": ["divisibility", "modular-arithmetic", "math-rules"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "number": { "type": "integer", "description": "Integer to test" }
        },
        "required": ["number"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:prime-check-tool",
      "displayName": "Prime Number Checker & Primality Test",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/prime-check",
      "description": "Deterministic primality testing verifying whether an integer is prime or composite, with smallest non-trivial divisor proofs.",
      "tags": ["prime-checker", "primality", "number-theory"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "number": { "type": "integer", "description": "Number to test for primality" }
        },
        "required": ["number"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:sqrt-factor-calculator",
      "displayName": "Square Root Radical Simplifier",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/sqrt-factor",
      "description": "Extracts the largest perfect square factors from a radicand to simplify square roots into simplest radical form a*sqrt(b).",
      "tags": ["radicals", "square-root", "simplifying-radicals", "algebra"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "radicand": { "type": "integer", "description": "Number inside the radical" }
        },
        "required": ["radicand"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:tool:common-denominator-calculator",
      "displayName": "Least Common Denominator (LCD) Calculator",
      "type": "application/tool+json",
      "url": "https://factorcalculators.com/common-denominator",
      "description": "Determines the least common denominator among two or more fractions using LCM of denominators, converting fractions to equivalent common bases.",
      "tags": ["lcd", "fractions", "common-denominator", "arithmetic"],
      "inputSchema": {
        "type": "object",
        "properties": {
          "fractions": {
            "type": "array",
            "items": { "type": "string" },
            "description": "Array of fractions, e.g. ['1/4', '2/5', '5/6']"
          }
        },
        "required": ["fractions"]
      }
    },
    {
      "identifier": "urn:air:factorcalculators.com:doc:llms-txt",
      "displayName": "LLMs.txt Mathematical Reference",
      "type": "text/markdown",
      "url": "https://factorcalculators.com/llms.txt",
      "description": "Machine-optimized roadmap, formulas, and guidance for Large Language Models querying factorcalculators.com.",
      "tags": ["llms.txt", "context", "ai-guidance"]
    },
    {
      "identifier": "urn:air:factorcalculators.com:dataset:math-guides",
      "displayName": "Educational Math Knowledge Base",
      "type": "application/json",
      "url": "https://factorcalculators.com/blog",
      "description": "Curated library of 16 in-depth educational math guides covering factoring, prime decomposition, GCF/LCM algorithms, and radical simplifications.",
      "tags": ["educational", "math-tutorials", "articles"]
    }
  ]
}