 Hello and welcome to the session. Today I'll help you with the following question. The question says use Euclid's division algorithm to find the hcf of 135 and 225. First let's see what Euclid's division algorithm is. To obtain the hcf of two positive integers, say c and d, with c greater than d, follow these steps below. First let's see what Euclid's division lemma is. It says given positive integers a and b, there exist unique integers q and r, satisfying a equal to bq plus r, where r is greater than equal to 0 and r is less than b. Now the step one of the algorithm says that apply Euclid's division lemma to c and d, so we find whole numbers q and r such that c is equal to dq plus r, where r is greater than equal to 0 and less than d. Then the step two says if r is equal to 0, d is the hcf of c and d and if r is not equal to 0, apply the division lemma to d and r. Next step, the step three is continue the process till the remainder is 0. The divisor at this stage will be required hcf. Now let's move on to the solution. We are supposed to find the hcf of 135 and 225. Now we should apply the Euclid's division algorithm to find the hcf of these two numbers. In the first step of this as you can see we apply the Euclid's division lemma. For this we will take c as 225 and d as 135 as it is required that c should be greater than d. Then we have c is equal to dq plus r. So we have 225 when divided by 135 we get 1 as the question and 90 as the remainder. Thus we substitute the values of c and d in this. We get 225 is equal to 135 multiplied by q which is 1 that is the question plus r that is the remainder and that is 90. Here we have r is equal to 90 which is not equal to 0. So again we apply Euclid's division lemma to 135 and 90. So we get 135 is equal to 90 then we divide 135 by 90 1 as the question and 45 as the remainder. So here we have 135 is equal to 90 multiplied by the question that is 1 plus the remainder that is 45. As you can see here r is equal to 45 which is not equal to 0. So we apply Euclid's division lemma to 90 and 45. So we get 90 is equal to 45 then again we divide 90 by 45 so we get 2 as the question and 0 as the remainder. So here we get 90 is equal to 45 multiplied by the question that is 2 plus the remainder that is 0. Now as you can see here we have r is equal to 0. Let's recall the step 3 again which says that we continue the process till the remainder is 0 then the divisor at this stage will be the required hcf. Here we get remainder r is equal to 0 and the divisor in this case is 45. So we say that 45 is the hcf of 135 and 225. So the final answer is 45. So hope you enjoyed the session have a good day.