Integer prime factors

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

Compute the prime factorization of a positive integer as a list of prime/exponent pairs.

Use when you need to: integer prime factors · prime factorization · factorize integer.

Supported

• integer prime factors
• prime factorization
• factorize integer

Not supported

• factorization of 0 or negative integers
• probabilistic factorization
• divisor listing

Behavior

• value is a canonical positive integer string from 1 to 1000000000000 (10^12) inclusive.
• 0 and negative values are rejected: prime factorization is only defined here for positive integers.
• value 1 returns an empty factors array (the empty product).
• factors is sorted ascending by prime, each entry { prime, exponent } with prime a canonical positive integer string and exponent a positive JSON integer.
• Every listed prime, multiplied by itself exponent times across all entries, reconstructs value exactly.
• Factorization uses exact trial division up to sqrt(value), bounded by the 10^12 input cap for predictable running time.

Input

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

Output

• factors (array of object, required)

Limits

• max value: 1000000000000
• max digits: 13

Example

Request input:

{
  "value": "360"
}

Response:

{
  "result": {
    "factors": [
      {
        "prime": "2",
        "exponent": 3
      },
      {
        "prime": "3",
        "exponent": 2
      },
      {
        "prime": "5",
        "exponent": 1
      }
    ]
  }
}

How to call it

MCP

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

{
  "id": "integer-prime-factors",
  "version": "1.0.0",
  "input": {
    "value": "360"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-prime-factors/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"value":"360"}'

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

CLI

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

Get the client at /clients/cli/.

Related tools

• Integer divisors: List every positive divisor of a positive integer, ascending.
• Integer is prime: Deterministically test whether a non-negative integer string is prime.
• Array integer adjacent diff: Replace an array of canonical integer strings with consecutive first differences.
• Array integer clamp: Clamp an array of canonical integer strings to optional inclusive min and max bounds.
• Array integer cumulative sum: Replace an array of canonical integer strings with equal-length prefix sums.
• Array integer GCD: Compute the non-negative greatest common divisor of an array of canonical integer strings.