Integer divisors

integer-divisors · version 1.0.0 · Numbers & math · free, no key needed

List every positive divisor of a positive integer, ascending.

Use when you need to: integer divisors · list divisors · all factors of a number.

Supported

• integer divisors
• list divisors
• all factors of a number

Not supported

• divisors of 0 or negative integers
• divisor count only
• sum of divisors

Behavior

• 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).

Input

• value (string, required): max length 13; pattern ^[1-9][0-9]*$

Output

• divisors (array of string, required)

Limits

• max value: 1000000000000
• max digits: 13
• max divisors output: 100000

Example

Request input:

{
  "value": "12"
}

Response:

{
  "result": {
    "divisors": [
      "1",
      "2",
      "3",
      "4",
      "6",
      "12"
    ]
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "integer-divisors",
  "version": "1.0.0",
  "input": {
    "value": "12"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-divisors/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"value":"12"}'

The machine-readable contract is at /v1/tools/integer-divisors/versions/1.0.0.

CLI

node cli.mjs run integer-divisors 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Array integer GCD: Compute the non-negative greatest common divisor of an array of canonical integer strings.
• Array integer LCM: Compute the non-negative least common multiple of an array of canonical integer strings.
• Array integer median: Select lower and upper middle canonical integers; emit median only for odd length.
• Array rational sum: Sum an array of canonical rationals and return the reduced total.
• Integer digit sum: Sum the base-b digits of the magnitude of an integer string.
• Integer is perfect square: Test whether a non-negative integer string is a perfect square.