The process of dividing one integer by another to produce a unique quotient and remainder, where the remainder is always less than the divisor. Also known as the division algorithm, it states that for integers a and b (b > 0), there exist unique integers q and r such that a = bq + r and 0 ≤ r < b.
Named after the ancient Greek mathematician Euclid (c. 300 BCE), though the algorithm was known earlier. The term became standard in the 19th century when mathematicians began formalizing arithmetic operations and their properties in abstract algebra.
Euclidean division is the mathematical foundation that makes modular arithmetic possible, powering everything from computer algorithms to cryptography! It's amazing that this ancient Greek insight about remainders now secures our digital communications and online banking.
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