Given:a3 - 1 and a2 - 1Concept:The greatest common divisor (GCD) refers to the greatest positive integer that is a common divisor for a given set of positive integers. It is also termed as the highest common factor (HCF) or the greatest common factor (GCF)Calculation:? we know formulas,? a3 - b3 = (a - b)(a2 + ab + b2)? a2 - b2 = (a + b)(a - b)? taking a3-1 instead of a3 -b3? replacing b by 1? in both of above equations? a3 - 1 = (a-1)(a2 + a + 1)? a2 - 1 = (a + 1)(a - 1)we can clearly see that The common factor is (a - 1).