Find the largest number which will divide 415, 756 and 1035 leaves the remainder same in each case.

25 31 35 43

31

We need to find the HCF of: (756 - 415) and (1035 - 756) = 341 , 279 ⇒ HCF of  341 and  279 = 31 Therefore, 31 is the largest number which will divide 415, 756 and 1035 and leaves the same remainder in each case.