division algorithm: meaning, definition, pronunciation and examples

No. While its most common form is for integers, a completely analogous Division Algorithm exists for polynomials (with the condition on the remainder being that its degree is less than the divisor's degree).

Long division is a specific, well-known computational procedure (an algorithm) for implementing division. The Division Algorithm is the general mathematical theorem that states such a procedure will always produce a unique quotient and remainder meeting specific criteria. Long division is one instantiation of this theorem.

Historically, the term derives from the step-by-step procedure (algorithm) of long division. The associated theorem, which proves the correctness and uniqueness of the result of that procedure, inherited the name. This is a case where the name for the process and the name for the underlying theoretical principle are identical.

Yes, but the standard statement requires the divisor to be positive. For a positive divisor, the theorem holds for any integer dividend (positive, negative, or zero), guaranteeing a unique non-negative remainder less than the divisor. If the divisor is negative, one usually applies the algorithm with its absolute value and adjusts signs accordingly.

A step-by-step procedure or method for performing division between numbers or polynomials, resulting in a quotient and remainder.

Division algorithm is usually formal / technical / academic in register.

Division algorithm: in British English it is pronounced /dɪˈvɪʒ.ən ˈæl.ɡə.rɪ.ðəm/, and in American English it is pronounced /dɪˈvɪʒ.ən ˈæl.ɡə.rɪ.ðəm/. Tap the audio buttons above to hear it.