The question is to find the greatest number which when divides 1750 and 2000 leaves remainder 48 and 2 resp. So, can we take it as if we remove 48 and 2 from 1750 and 2000 resp, there will be no remainder ? So after removing the remainders, the numbers are :-
1702 and 1998.
So, now that greatest common number divides both 1702 and 1998 completely. Now find that common number, and that common greatest number is called HCF [Highest Common Factor]. THe HCF of 1702 and 1998 is 74.
So 74 divides 1702 and 1998 COMPLETELY.
Now, we can check if we got the answer. If we add 48 extra to 1702 and 2 extra to 1998, we get remainder 48 and 2 resp. [both 48 and 2 < 74].
So thats the answer with explanation.