| Question3. Differentiate between Eulids division lemma and Euclids division algorithm |
| Answer. Eulids division lemma states that for two given positive integers a and b. there exist unique integers q and r satisfying a = bq + r, 0 <= r < b. Whereas Euclid's Division algorithm is used to obtain the HCF of two positive integers, say a and b, with a > b, follow the steps below: # Apply Euclid's division lemma, to a and b. So, we find whole numbers, q and r such that a = bq + r, 0 < = r < b. # If r = 0, b is the HCF of a and b. If r not equal to 0, apply the division lemma to b and r. # Continue the process till the remainder is zero. the divisor at this stage will be the required HCF. |