Question

What is Euclid's division lemma,give one example?

Answer 1

Answer:

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. b is the divisor. q is the quotient and r is the remainder. By using this lemma, we can find the HCF of two numbers.

For example:-

To find the HCF of  272 and 1032 :-

Start with the larger integer, that is 1032, Apply the division Lemma to 1032 and 272, we get

1032 = 272 × 3 + 216

Since , the remainder 216 ≠ 0.

We apply the division Lemma to 272 and 216, we get

272 = 216 × 1 + 56

Remainder 56≠0

216 = 56 × 3 + 48

Remainder 48≠0

56 = 48 × 1 + 8

Remainder ≠ 0

48 = 8 × 6 + 0

The remainder has now become zero ,so our procedure stops.

Since , the divisor at this stage is 8 , the HCF of 1032 is 272 is 8.

Step-by-step explanation:

Answer 2

Answer:

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. ... In this example, 9 is the divisor, 58 is the dividend, 6 is the quotient and 4 is the remainder.