submultiple

Submultiple is a term used in mathematics and metrology to describe a relation of a quantity to another. In mathematics, a submultiple of a positive integer n is any positive divisor of n. In practice this means that every submultiple of n is a number that divides n exactly, and the term is largely synonymous with divisor or factor. For example, the submultiples of 12 are 1, 2, 3, 4, 6, and 12. A number has a finite set of submultiples, and the total number of submultiples is determined by its prime factorization n = p1^a1 ... pk^ak, yielding (a1+1)(a2+1)...(ak+1) divisors.

In metrology, submultiples refer to decimal fractions of a base unit. The SI system and common practice use prefixes such as deci (0.1), centi (0.01), milli (0.001) and smaller to form submultiples of units like the meter, liter, or gram. Examples include the centimeter (0.01 meter), the millisecond (0.001 second), and the microgram (1e-6 gram). Submultiples provide convenient naming for measurements that are smaller than the base unit without resorting to full decimal notation.

Usage notes: the term is more common in older mathematical literature and in some educational contexts, where divisor or factor is preferred in modern terminology. In measurement and metrology, submultiples are a standard concept describing parts of a base unit, typically expressed through official prefixes and symbols. Overall, submultiples bridge numeric divisibility and practical unit scaling, depending on context.