 Hello friends, welcome to the session I am welcome. We are going to discuss real numbers. A given question is used Euclid's division algorithm to find the hcf of 196 and 38,220. So let me tell you the basic idea which is Euclid's division algorithm to obtain the hcf of c and d where c is more than d. We will apply Euclid's division lemma to c and d. We find two whole numbers q and r such that on dividing c by d we get q as the question and r is the remainder where r is always more than n equal to 0 which it should always be less than d. If r equal to 0 this implies that d is the hcf of c and d but if r is not equal to 0 then we will apply the division lemma to d and r and this process keeps on going till r equal to 0 and at that stage where r is equal to 0 d is the required hcf. So now let's start with the solution. We have to find the hcf of 196 and 38,220. So here we see that c equal to 38,220 and d equal to 196. As we know that c should always be more than d. Now we will apply Euclid's division algorithm. From this we can say that c equal to dq plus r where c is 38,220 on dividing 38,220 by 196 we get question as 195 with the remainder as 0. So here we see that r equal to 0 this implies that d which is 196 is the hcf thus 196 and 38,220 is 196. So hope you understood the solution and enjoyed the session. Goodbye and take care.