Highly Composite Number Checker

This checker applies that strict record-setting definition to the value you provide, rather than merely deciding whether the value has many factors or is composite. It returns the divisor count for the selected number, the greatest divisor count attained below it, and a direct true-or-false result. That supporting detail makes the decision easy to inspect in lessons, integer-sequence research, programming exercises, and validation pipelines.

What the highly composite test means

A number qualifies only when its count of positive divisors is strictly greater than the divisor count of every smaller positive integer. The word strictly matters. If an earlier value already reached the same count, the later value does not establish a new record and the checker returns false. For example, the method is concerned with record holders in the divisor-count sequence, not with the everyday distinction between prime and composite numbers. The positive integer 1 is included: it has one positive divisor, while there are no smaller positive integers to beat, so it is the first record holder under the standard definition used here. The result includes divisor_count for the submitted value and max_smaller_divisor_count for the best earlier value. Comparing those two fields explains the Boolean answer without requiring trust in an unexplained label. This is especially useful when studying record sequences, where a near miss may have an impressive factorization but still fail because an earlier integer tied or exceeded its divisor count.

How the checker reaches a deterministic answer

The algorithm creates an exact divisor-count table for every positive integer from 1 through the requested value. It visits each possible divisor and increments the count of each multiple, which is the same relationship expressed by saying that a divisor divides a number with no remainder. After the table is complete, the checker scans all entries below the requested value and records the largest divisor count it finds. The submitted number is highly composite precisely when its own count is larger than that earlier maximum. No probabilistic primality test, approximation, remote database, random choice, or clock-dependent value is involved. Identical input therefore produces identical JSON in the browser and through the API. The implementation accepts positive safe integers and digit-only text representing them. It rejects fractions, nonnumeric text, values below one, and inputs above the declared bound. The bound keeps both memory use and the nested arithmetic loops predictable in a browser or edge runtime while remaining large enough for exploration and routine sequence checks.

Reading and using the returned fields

Start with is_highly_composite, the primary decision. When it is true, divisor_count is necessarily greater than max_smaller_divisor_count, showing that the input has established a new record. When it is false, the previous maximum is equal to or greater than the input's count, so the input cannot satisfy the definition even if it has many factors. The response also repeats n, which helps logs and batch jobs keep each decision attached to its source value. For a sequence lesson, submit neighboring integers and watch the maximum remain fixed until a new record arrives. For software tests, assert both the Boolean and the two counts so a regression cannot hide behind a correct-looking label. For data pipelines, treat an invalid-input response as a contract failure rather than a mathematical result; zero and negative integers are outside the domain. Each API request costs $0.002, while the browser version runs locally. Neither route sends a lookup request to an outside number database, and neither changes or stores the submitted integer.