Question

Find the largest number which divides 286 and 1250 leaving a remainder of 10 and 8 in each case

Answer 1

well the question here asks for you to find the HCF(highest common factor) as it says "the greatest number which divides"
Now to solve this, first you need to subtract the given remainders from their given respective terms :
286 - 10 = 276
and 1250 - 8 = 1242
Now as we have these two new numbers, we need to find the HCF of them :
by using Euclid's division lemma, 
a=bq+r , where b>r>or=0
(this can also be solved by taking out the common factors of both the numbers) 
in this case, a=1242 , b=276
1242 = 276 × 4 + 138
276=138×2+0
as the remainder is now zero, therefore 138 is the required number

^_^ hope this helps!