What is the largest number that divides 460, 491 and 553, and leaves remainder 26 in each case?

31

      460       491       553

         ↓        ↓  ↓         ↓

             ↓             ↓

            31           93     (difference)

⇒ HCF of 31 and 93 is 31

Hence, 31 the largest number that divides 460, 491 and 553, and leaves remainder 26 in each case.