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

Annotations already declare readOnlyHint, idempotentHint and closed-world, so the safety profile is covered. The description adds real behavioral value beyond that: the output includes each prime factorization, and there is a 20-number input ceiling not visible from the annotations.

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?

Roughly three short sentences, no padding. Leading with the worked example is slightly indirect for an agent scanning for the verb, but it is compact and informative. The trailing web-page URL is promotional rather than operational and is the only dispensable element.

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, no-output-schema tool this is nearly complete: it describes what is computed and that prime factorizations are returned. It omits behavior on malformed input (non-integers, duplicates, out-of-range values), which is the main remaining gap.

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?

With a single parameter at 100% schema coverage, the baseline is 3. The description's 'up to 20 whole numbers' restates what the schema already says ('Whole numbers 2 to 20...'), and the comma/space delimiter guidance is also in the schema, so little is added.

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?

The description names the specific computation (GCD/GCF and LCM/HCF) and reinforces it with a worked example, so an agent knows exactly what the tool produces. It does not explicitly contrast with near-neighbors like prime_number_checker or fraction_calculator, but the resource is distinctive enough to stand apart.

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 only implied by the nature of the tool; there is no statement of when to prefer it over alternatives (e.g., prime_number_checker when you only need factor structure). It does communicate scope ('up to 20 whole numbers') and the GCF/HCF synonym, which gives the agent some selection context.

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