kertoluku

Kertoluku is a Finnish mathematical term that denotes the product obtained by multiplying two or more numbers. In arithmetic, the kertoluku of numbers a1, a2, ..., an is the value a1 × a2 × ... × an. The operation that yields a kertoluku is multiplication, and the numbers being multiplied are called factors or multiplicands.

Etymology and usage: The word combines kerta, meaning a counting of times, with luku, meaning number. It is used mainly in educational contexts to discuss the result of multiplication, though in many texts the term product is used more frequently.

Properties: The kertoluku mirrors standard properties of multiplication. It is commutative (ab = ba) and associative ((ab)c = a(bc)). It distributes over addition (a(b + c) = ab + ac). If any factor is zero, the kertoluku is zero; multiplying by one leaves the kertoluku unchanged. The sign of a kertoluku depends on the number of negative factors.

Notation and computation: Kertoluku can be written with a dot, a times sign, or simply by adjoining factors (e.g., 3 · 4, 3 × 4, or 3 4). For a sequence of numbers, the kertoluku is the product of all terms.

Applications: Kertoluku is a fundamental concept in algebra, number theory, probability, and combinatorics, used to simplify expressions, factorize numbers, and compute probabilities or counts that involve multiplicative reasoning.

See also: Multiplication, Product, Prime factorization.