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...'', resulting from division of ''a'' by ''b''. This is the basis for the [[Euclidean algorithm]] for computing [[greatest common divisor]]s.

...is not immediately obvious. In fact, it is a significant result.<ref>The [[Euclidean algorithm]] may be used to show that <math>\scriptstyle\mathbb{Z}</math> is a [[princ

(the [[Euclidean algorithm]]; ''Elements'', Prop. VII.2) and the first known proof of the [[infinitude ...t., p. 42).</ref> this is a procedure close to (a generalisation of) the [[Euclidean algorithm]], which was probably discovered