Integer digital root

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

Repeatedly sum the base-b digits of the magnitude of an integer string until a single digit remains.

Use when you need to: integer digital root · repeated digit sum · digital root in a base.

Supported

• integer digital root
• repeated digit sum
• digital root in a base

Not supported

• single-pass digit sum
• digital root of a fraction
• casting out nines shortcut only

Behavior

• value is a canonical integer string: 0 or an optional ASCII minus followed by a non-zero leading digit, at most 1000 digits excluding sign.
• base is a JSON integer from 2 to 36; when omitted it defaults to 10.
• The sign of value is ignored: the digital root is computed on the magnitude |value|.
• value 0 has digital root 0 in every base.
• The base-b digit sum is repeated until the result is a single base-b digit, i.e. strictly less than base.
• digital_root is returned as a JSON integer in [0, base).

Input

• value (string, required): max length 1001
• base (integer, optional): min 2; max 36; default 10

Output

• digital_root (integer, required): min 0

Limits

• max digits: 1000
• min base: 2
• max base: 36

Example

Request input:

{
  "value": "9875"
}

Response:

{
  "result": {
    "digital_root": 2
  }
}

How to call it

MCP

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

{
  "id": "integer-digital-root",
  "version": "1.0.0",
  "input": {
    "value": "9875"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-digital-root/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"value":"9875"}'

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

CLI

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

Get the client at /clients/cli/.

Related tools

• Integer digit sum: Sum the base-b digits of the magnitude of an integer string.
• 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.
• Array integer LCM: Compute the non-negative least common multiple of an array of canonical integer strings.
• Array integer sum: Sum an array of canonical integer strings and return the canonical total.
• Array rational sum: Sum an array of canonical rationals and return the reduced total.