Question

what. is mean by euchid division lemma. I follow who give answer quickly​

Answer 1

Euclid's Division Lemma: An Introduction. According to Euclid's Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b. ... HCF is the largest number which exactly divides two or more positive integers.

By dividing both the integers x and y the remainder is zero. Definition: Euclid's Division Lemma states that, if two positive integers “a” and “b”, then there exists unique integers “q” and “r” such that which satisfies the condition a = bq + r where 0 ≤ r ≤ b.

Euclid's Division Algorithm states that the divided is equal to product of the divisor and quotient added to the remainder. Where, Quotient is denoted by q and the remainder is denoted by r. ☸️ HCF * LCM = PRODUCT OF THE TWO NUMBERS.

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Answer 2

Euclid's division lemma is based on the very basic thing which we learn in class4 or 5 that is "division". It's simply based on division.

$\bold {Euclid's \ Division \ lemma}$

Given positive integer 'a' and 'b' , there exist unique integer 'q' and 'r' satisfying following lemma:

$a=b \times q +r, where\ 0 \leqslant r < b$

That's all what Euclid's lemma is.

Now , we have two things Euclid's

• Euclid's lemma
• Euclid's algorithm

We get confused between two. So lets clear right here.

• Lemma : It is a proven statement used for proving another statement.
• Algorithm : It is a series of well defined step which gives a procedure for solving a type of problem.

ExAmple of Euclid's lemmA:

7= 2×3+1