Equidigital Number Checker

This checker factors any supported integer, counts the digits in every prime and every written exponent, and compares that total with the digits in the original number. It returns the complete structured factorization alongside both counts, making the decision transparent and easy to verify in lessons, puzzles, scripts, and number theory experiments.

What the equidigital test measures

The test compares two compact descriptions of the same positive integer. The first description is simply the integer written in base ten, so its size is the number of decimal digits in n. The second is its canonical prime factorization. For that description, the checker counts every digit used by each prime base and also counts the digits of an exponent whenever that exponent is greater than one. An exponent of one is conventionally omitted, so it contributes nothing. Multiplication signs and exponent punctuation are notation rather than digits and are not counted. For example, 27 has two decimal digits and factors as 3 raised to the third power. The base 3 contributes one digit and the exponent 3 contributes one more, making 27 equidigital. The response includes both totals rather than returning only a label, which lets you audit the result and reuse the factorization in another calculation. Values below two are rejected because this classification is defined here through a nonempty prime factorization.

How to read the factorization result

Submit n as an integer, not as formatted text, a decimal, or scientific notation. The response lists factorization entries in ascending prime order. Each entry contains a prime and its exponent, including an explicit exponent of one in the structured output even though that one is omitted when counting written factorization digits. The number_digits field reports the length of the original decimal integer. The factorization_digits field adds the decimal length of every prime base and, only for repeated factors, the decimal length of its exponent. Finally, is_equidigital is true exactly when those two totals match. This representation avoids ambiguity around factors such as 101, whose prime base itself occupies three digits, and large exponents such as 12, whose exponent occupies two. It also makes multiplication symbols irrelevant to the calculation. The checker accepts values through one trillion. That explicit ceiling keeps execution predictable for prime inputs, which require the most trial divisors, while covering a useful range for classroom examples, programming exercises, and exploratory sequences.

Use the classification carefully

Equidigital is one member of a related family of digit classifications. If a prime factorization needs fewer digits than the original number, the number is often called economical; if it needs more, it is extravagant. Some references further reserve the word frugal for a stricter economical case. This capability answers only the equality question and exposes the counts so you can apply any broader terminology your source requires. It uses ordinary decimal notation and the unique prime factorization, so it does not compare alternate bases or expanded products with repeated copies of the same prime. Because the algorithm is deterministic and performs no network calls, the same valid input always produces the same ordered factors and decision. That property is useful when building test fixtures or checking a generated sequence. For API automation, each request costs $0.002; the browser execution uses the same pure solving logic. When comparing results with a textbook or online sequence, confirm that the other source also omits exponent one and ignores multiplication and exponent symbols, since different display conventions can otherwise appear to disagree.