elementairdeelbaar

Elementairdeelbaar is a term used in some Dutch mathematical education to describe a natural number that is divisible by a specified set of elementary divisors, typically small primes or other simple numbers. The idea is to consider numbers that satisfy several straightforward divisibility requirements at once.

Definition and notation

Let D = {d1, d2, ..., dk} be a finite set of positive integers called elementary divisors. A natural number n is elementairdeelbaar with respect to D if n is divisible by every di in D. Equivalently, n must be a multiple of the least common multiple of the set, lcm(d1, d2, ..., dk). If the elements of D are pairwise coprime, this is the same as n being a multiple of the product d1 d2 ... dk.

Examples

If D = {2, 3, 5}, then any multiple of 30 is elementairdeelbaar with respect to D (for instance, 60, 90, 120). If D = {4, 6}, the condition is that n be a multiple of lcm(4, 6) = 12, so 12, 24, 36, etc. The product 4×6 = 24 is only equivalent when the numbers are pairwise coprime; otherwise the lcm governs the required multiple.

Relation to broader concepts

Elementairdeelbaar connects to divisibility, least common multiples, and prime factorization. When D consists of the first m primes, the required multiples are governed by the primorial, the product of those primes. The concept is mainly used as a pedagogical tool to illustrate how multiple divisibility conditions interact.

Notes

Elementairdeelbaar is not a formal, universally standard term in all mathematical texts; its usage varies by curriculum and context. See also divisibility, least common multiple, primorial, and prime numbers.