 Hello and welcome to the session. In this session we discussed the following question which says find the greatest number which divides 401 and 1085 leaving the remainder 5 in each case. Now let's see the solution. So we have to find the greatest number which divides 401 and leaves the remainder 5. Also the same greatest number divides 1085 leaving the remainder 5. So we say that we find the greatest number which divides 401 minus the remainder that is 51085 minus the remainder which is 5 and this greatest number should divide both these numbers exactly. That is we find the greatest number which divides 401 minus 5 which is 3961085 minus 5 which is 1088. So the required greatest number is given by the HCF of 396 and 1080. So by finding the HCF of the numbers 396 and 1080 we get the greatest number which divides 401 and 1085 leaving the remainder 5 in each case. To find the HCF of these two numbers what we do is first we divide the greater number that is 1080 by the smaller number that is 396. We have 396 2 times is 792 then we subtract 792 from 1080 we get 288 as the remainder. Next we will divide the divisor which is 396 by this remainder 288. So 396 is divided by 288 and we have 288 one time is 288 we subtract 288 from 396 and we get 108 as the remainder. So we will keep repeating the process of dividing the preceding divisor by the remainder last obtained till we obtain remainder as 0. So in the same way we divide the divisor which is 288 by the remainder 108. Now 108 2 times is 216 216 is subtracted from 288 to get the remainder as 72 then again we divide the divisor that is 108 by the remainder 72 and 72 one time is 72 we subtract 72 from 108 to get the remainder as 36. Now the divisor 72 is divided by the remainder 36 and we know 36 2 times is 72 and we get the remainder as 0. Now we have got the remainder as 0 so we will stop here itself and the last divisor that is 36 is the required HCF of the given numbers. So we say HCF of 396 and 1080 is 36 the greatest number which divides 401 and 1085 leaving remainder 5 in each case is 36. 36 is our final answer this completes the session hope you have understood the solution of this question.