Question

what do you mean by Euclid division lemma
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Answer 1

A lemma is a proven statement used for proving another statement. So, according to Euclid's Division Lemma, if we have two positive integers a and b, then there would be whole numbers q and r that satisfy the equation: a = bq + r, where Osr<b. a is the dividend... q is the quotient and r is the remainder.

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Answer 2

Answer:

A lemma is a proven statement used for proving another statement. So, according to Euclid's Division Lemma, if we have two positive integers a and b, then there would be whole numbers q and r that satisfy the equation: a = bq + r, where 0 ≤ r < b. a is the dividend. ... q is the quotient and r is the remainder.

Explanation:

example

Consider two numbers 78 and 980 and we need to find the HCF of these numbers. To do this, we choose the largest integer first, i.e. 980 and then according to Euclid Division Lemma, a = bq + r where 0 ≤ r < b;

980 = 78 × 12 + 44

Now, here a = 980, b = 78, q = 12 and r = 44.

Now consider the divisor 78 and the remainder 44, apply Euclid division lemma again.

78 = 44 × 1 + 34

Similarly, consider the divisor 44 and the remainder 34, apply Euclid division lemma to 44 and 34.

44 = 34 × 1 + 10

Following the same procedure again,

34 = 10 × 3 + 4

10 = 4 × 2 + 2

4 = 2 × 2 + 0