Prime Factorization

Break any number into its prime factors.

Prime factorisation underpins the modular arithmetic behind public-key encryption, and the greatest common factor is what reduces a fraction to lowest terms. Binary, octal and hexadecimal are simply place-value systems running on a different base.

Number-theory answers follow from prime structure: factors, multiples, remainders and repeating cycles all come out of the way a number breaks into primes. Binary, notation and sequence questions are the same idea in another base or another form.

Every whole number above one is either prime or the product of primes in exactly one way, which is what makes factorisation a fingerprint. Public-key cryptography rests on multiplying two large primes being easy while recovering them is not.

Whole-number results here are exact rather than rounded, so a value that looks wrong is almost always a unit or base mismatch rather than a rounding artefact.

Factors and multiples carry the structure of a number: the greatest common factor is the largest block two numbers share, and the least common multiple is the smallest in which both fit. Base conversion preserves value while changing the symbols used to write it.

Prime Factorization sits with the rest of the library's maths work, and it rests on the same whole-number arithmetic the way a textbook or an exam paper does. Its answer is only as good as the assumptions standing behind it.

The quantities it works from — number — are the ones a real whole-number question actually turns on, and each carries a convention of its own, set out below.

Mathematics is the one subject here that depends on nothing local: the same theorem holds in Ohio and Osaka, and the same fraction carries the same value everywhere. What changes is how results are written — American schooling teaches decimal notation and long division, and business arithmetic runs on fractions of a dollar.

Precision and rounding are where most practical errors creep in.