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IBM

MCP Math Server

by IBM

is_harshad_number

Check if a number is divisible by the sum of its digits (Harshad/Niven number) to verify this mathematical property in base 10 or other bases.

Instructions

Check if a number is a Harshad (Niven) number (divisible by sum of its digits). (Domain: arithmetic, Category: digital_operations)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
baseNo
Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It discloses the core behavior (checking divisibility by digit sum) and mentions an optional 'base' parameter implicitly via the domain hint. However, it lacks details on edge cases (e.g., negative numbers, zero), performance, error handling, or output format, leaving gaps in behavioral context.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. Every word earns its place, with no redundant or vague phrasing, making it efficient and easy to parse.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's low complexity (a mathematical check), no annotations, no output schema, and 0% schema coverage, the description is minimally adequate. It covers the core functionality but omits details on parameters, return values, and edge cases. It meets basic needs but lacks depth for full contextual understanding.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% description coverage, but the description compensates well. It explains the primary parameter 'n' as the number to check and implies 'base' through the mathematical context (Harshad numbers are base-dependent). While not detailing exact usage, it adds meaningful semantics beyond the bare schema, justifying a high score.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Check if a number is a Harshad (Niven) number (divisible by sum of its digits).' It specifies the verb ('check'), resource ('number'), and mathematical definition. However, it does not explicitly differentiate from sibling tools like 'harshad_numbers' (which likely lists them) or other number property checkers, keeping it from a perfect score.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('digital_operations'), but does not specify contexts, prerequisites, or compare to similar tools like 'is_perfect_number' or 'is_palindromic_number'. This lack of explicit usage instructions limits its helpfulness.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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