Question

What is Euclid Division Algorithm

Answer 1

In arithmetic, Euclidean division is the process of division of two integers, which produces a quotient and a remainder smaller than the divisor. Its main property is that the quotient and remainder exist and are unique, under some conditions. .

Answer 2

Answer:

For any two positive integers a and b, there exist unique integers q and r satisfying a=bq+r, 0≤ r <b.

Step-by-step explanation:

To obtain the HCF of two positive integers, say c and d, with c > d, follow the steps below:  

Step 1 : Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and r such that c = dq + r, 0 ≤ r < d.  

Step 2 : If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.  

Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.  

This algorithm works because HCF (c, d) = HCF (d, r) where the symbol HCF (c, d) denotes the HCF of c and d, etc.

Hope this will help you.. :)