Euclid’s Division Lemma:
Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.
Euclid’s division algorithm is based on this lemma.
An algorithm is a series of well defined steps which gives a procedure for solving a type of problem.
The word algorithm comes from the name of the 9th century Persian mathematician al-Khwarizmi. In fact, even the word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabrw’al muqabala. A lemma is a proven statement used for proving another statement.
Euclid’s division algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers.
Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.
Euclid’s division algorithm is based on this lemma.
An algorithm is a series of well defined steps which gives a procedure for solving a type of problem.
The word algorithm comes from the name of the 9th century Persian mathematician al-Khwarizmi. In fact, even the word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabrw’al muqabala. A lemma is a proven statement used for proving another statement.
Euclid’s division algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers.
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