. Euclid’s Division Lemma Euclid, one of the most important mathematicians wrote an important book named “Elements” in volumes. The first six volumes were devoted to Geometry and for this reason, Euclid is called the “Father of Geometry” . But in the next few volumes, he made fundamental contributions to understand the properties of numbers.
One among them is the “Euclid’s Divison Lemma”. This is a simplified version of the long division process that you were performing for division of numbers in earlier classes. Le us now discuss Euclid’s Lemma and its application through an Algorithm termed as “Euclid’s Division Algorithm”. Lemma is an auxiliary result used for proving an important theorem.
It is usually considered as a mini theorem. Theorem : Euclid’s Division Lemma Let a and b be any two positive integers. Then, there exist unique integers q and r such that a bq + , ≤ < b .