Find the G.C.D of a³ - 1 and a² - 1

Given:

a3 - 1 and a2 - 1

Concept:

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).