{"id":"integer-divisors","version":"1.0.0","description":"List every positive divisor of a positive integer, ascending.","supported_operations":["integer divisors","list divisors","all factors of a number"],"unsupported_operations":["divisors of 0 or negative integers","divisor count only","sum of divisors"],"semantics":["value is a canonical positive integer string from 1 to 1000000000000 (10^12) inclusive.","0 and negative values are rejected: divisors are only defined here for positive integers.","value 1 returns divisors [\"1\"].","divisors lists every positive integer that evenly divides value, ascending, as canonical integer strings, including 1 and value itself.","Derived from the exact prime factorization by trial division up to sqrt(value), bounded by the 10^12 input cap for predictable running time.","If value would have more than 100000 divisors the request is rejected rather than returning a truncated list (this cannot occur below the 10^12 cap for any tested value, but the guard exists for defense in depth)."],"limits":{"max_value":"1000000000000","max_digits":13,"max_divisors_output":100000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string","pattern":"^[1-9][0-9]*$","maxLength":13}}},"output_schema":{"type":"object","additionalProperties":false,"required":["divisors"],"properties":{"divisors":{"type":"array","items":{"type":"string"}}}},"examples":[{"input":{"value":"12"},"output":{"divisors":["1","2","3","4","6","12"]}}],"execute_url":"/v1/tools/integer-divisors/versions/1.0.0/execute"}