Find the largest number which will divide 410, 751 and 1030 and leaves the remainder 7 in each case.

31

To find the largest number that divides 410, 751, 1030 and leaves 7 remainder, we subtract 7 from each number, so they're perfectly divisible.

⇒ 403, 744, 1023

Using elimination method from options : 25, 45 can be eliminated, because these numbers can not divide the above numbers. 

Now check other two,

\(\frac{403}{31}\) ,   \(\frac{403}{23}\)

We can check,  31 is the only number which divides all numbers.

Therefore,

Ans. c) 31