dzielnika

Dzielnika is the genitive singular form of the Polish noun dzielnik, meaning divisor. In mathematics, a dzielnik of an integer n is any integer d such that n is divisible by d, i.e., there exists an integer k with n = d·k. The relation of divisibility is often written with the symbol d|n. Divisors are typically considered as positive numbers, with negative divisors corresponding to their positives.

Every nonzero integer n has a finite set of positive divisors; for example, the positive divisors of 12 are 1, 2, 3, 4, 6, and 12. The number 120 has 16 positive divisors. A special case is zero: any nonzero integer divides 0, since 0 = d·0 for any d ≠ 0.

Related concepts include the greatest common divisor (gcd) and the least common multiple (LCM). The gcd of a and b is the largest positive integer that divides both, and it can be found via the Euclidean algorithm or prime factorization. Prime factorization expresses a number as a product of primes raised to powers, and a number’s divisors can be derived from those exponents.

In other fields, dzielnik is used as “divider” in electronics and signal processing, for example dzielnik napięcia (voltage divider) or dzielnik częstotliwości (frequency divider).

Etymology: dzielnik comes from dzielić, “to divide.” In Polish, dzielnika appears mainly in genitive constructions, e.g., właściwości dzielnika or brak dzielnika.