delbarhet

Delbarhet, or divisibility, is a relation between integers that describes when one number evenly divides another. For integers a and b with b not equal to zero, we say that b divides a if there exists an integer k such that a = b times k. In this case, b is called a divisor of a and a is a multiple of b. The relation is written with the symbol and notation b | a.

Examples illustrate the idea. Since 12 = 3 × 4, we have 3 | 12. Also 36 = 6 × 6, so 6 | 36. Conversely, 14 is not divisible by 5, so 5 ∤ 14. A key special case concerns zero: for any nonzero b, b divides 0 because 0 = b × 0. However, 0 does not divide any nonzero number, and many sources treat 0 | 0 as undefined.

Delbarhet has several basic properties. It is transitive: if a | b and b | c, then a | c. It is reflexive for nonzero numbers: a | a holds for any a ≠ 0. Divisibility also relates to other notions such as divisors, multiples, prime numbers, and the greatest common divisor, which is the largest positive integer that divides two given integers. In practice, delbarhet underpins factorization, modular arithmetic, and various algorithms in number theory.