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

Annotations already declare the safe-read profile (readOnlyHint, idempotentHint, non-destructive, closed-world), so the description's added value is in disclosing arithmetic behavior: exact BigInt precision (no float error) and that prime factorizations are also returned. That is genuinely useful context beyond what annotations state, though it stops short of noting edge cases such as negative operands.

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

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

A single front-loaded sentence with zero filler; the operation, its input scope, and its precision/derived-output characteristics are all packed in without repetition.

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

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

For a one-parameter, deterministic math tool with a fully documented schema and an output schema present, the description covers everything needed: op, input domain, arithmetic guarantees, and that factorization output accompanies the result.

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

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

Schema description coverage is 100%, and the schema already documents the ±10^12 bound, the string-of-digits format, and the 2–20 item constraint. The description restates the 2–20 range but adds no format or edge-case meaning beyond the schema, so the baseline 3 applies.

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

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

States a specific verb and resource ('Compute the greatest common factor'), plus concrete scope ('2–20 integers') and method ('exact BigInt arithmetic and complete prime factorizations'). It does not explicitly name the natural sibling lcm_calculator, but the resource is self-distinguishing from the rest of the math siblings.

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

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

Usage is implied by the self-explanatory name and purpose; an agent can infer this is the tool for GCF computations. However, there is no explicit when-to-use guidance and no mention of lcm_calculator as the alternative for the complementary operation, so nothing routes the agent deliberately.

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