CONCEPT: Required number must be the HCF of the numbers which are exactly DIVISIBLE by it.Calculation:8178 – 1 = 81777971 – 2 = 7969Required number = HCF (8177, 7969)⇒ 8177 = 13 × 17 × 37⇒ 7969 = 13 × 613HCF = 13∴ Required greatest number = 13