Number Theory & Precision calculators

This is the Fundamental Theorem of Arithmetic: any integer greater than 1 breaks down into prime factors in exactly one way (ignoring order). It's why prime numbers are called the 'building blocks' of the integers: there is only ever one valid blueprint.

GCF (greatest common factor) simplifies fractions to lowest terms and splits quantities into equal groups. LCM (least common multiple) finds a common denominator when adding fractions and determines when repeating events, like two buses on different schedules, line up again.

It keeps very large or very small numbers readable and makes their scale immediately visible: 6.02 × 10²³ communicates the number of atoms in a mole far more clearly than writing out 23 digits, and makes comparing magnitudes across very different scales much easier.

It depends entirely on the field and the measurement. A chemistry experiment might target under 5%, while some physics measurements demand well under 1%. There's no universal threshold. Check the standard your specific context expects.

A transistor has two reliable states, on and off. They map directly onto the two binary digits 0 and 1. Decimal would require ten distinguishable voltage levels per digit instead of two, far less reliable to build and read at the speeds modern hardware runs at.

Each hex digit represents exactly four binary digits, so a 32-bit value becomes 8 readable hex characters instead of 32 ones and zeros, with none of decimal's awkward, non-power-of-two grouping. That clean mapping is why memory addresses and color codes are conventionally written in hex.

Check for a prefix or explicit label: programming languages commonly use 0x for hexadecimal and 0b for binary, and technical documentation usually states the base outright. The digits alone rarely disambiguate, since 100 is a valid value in every common base.

Yes: JavaScript's number type loses exact precision past about 9 quadrillion (2^53), and factorial-style growth hits that ceiling fast. A calculator that would silently return a wrong answer past that point refuses instead, rather than showing a confident but incorrect result.

Each term is the sum of the two before it, and the ratio of neighboring terms approaches the golden ratio, about 1.618. The sequence shows up in counting problems and in some natural growth patterns.

Divide it by every prime up to its square root. If none divides evenly, it is prime. For 97 you only need to test 2, 3, 5 and 7, since 11 squared is already 121.

List the prime factors of each number and multiply the ones they share, or use the Euclidean algorithm with repeated division.

No. A prime has exactly two distinct factors, and 1 has only one, so the smallest prime is 2.

Multiply each binary digit by a power of two based on its position and add the results, so 1011 equals 8 plus 2 plus 1, or 11.