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IBM

MCP Math Server

by IBM

divisors

Calculate all positive divisors of any integer, returning them in sorted order for number theory and arithmetic applications.

Instructions

Find all positive divisors of a number in sorted order. (Domain: arithmetic, Category: number_theory)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the output is 'sorted order', which is useful, but does not cover other important aspects such as error handling (e.g., for negative inputs), performance characteristics, or whether it handles large numbers efficiently. The description is minimal and lacks depth for a tool with no annotation support.

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 with two sentences that directly state the tool's function and domain. Every word earns its place, and it is front-loaded with the core purpose, making it easy to understand quickly without unnecessary details.

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 (1 parameter, no output schema, no annotations), the description is adequate but minimal. It covers the basic purpose and output order, but for a tool with no annotations, it should ideally include more behavioral context (e.g., input validation, performance notes). The lack of output schema means the description doesn't explain return values, which is a gap.

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

Parameters3/5

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

The input schema has 1 parameter with 0% description coverage, so the description must compensate. It adds meaning by specifying that the parameter 'n' is a 'number' for which divisors are found, but does not detail constraints (e.g., must be positive integer, range limits) or provide examples. This is a baseline score as the description offers some context but not enough to fully document the parameter.

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

Purpose5/5

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

The description clearly states the tool's purpose with a specific verb ('Find') and resource ('all positive divisors of a number'), and specifies the output order ('sorted order'). It also distinguishes itself from sibling tools like 'divisor_count' or 'divisor_sum' by focusing on listing divisors rather than counting or summing them.

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

Usage Guidelines3/5

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

The description implies usage through the domain and category tags ('arithmetic, number_theory'), suggesting it's for mathematical computations. However, it does not explicitly state when to use this tool versus alternatives like 'divisor_count' or 'divisor_sum', nor does it provide any exclusions or prerequisites.

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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