UPSC 2015 CDS II Math Paper

(n3−n)(n−2)
=n(n2−1)(n−2)
=(n−2)(n−1)n(n+1)
Remember:
The product of four consecutive natural numbers is always divisible by 24.
For any natural number, n>2,(n–2)(n–1)n(n+1) is always expressed as the product of four consecutive natural numbers.
Thus, the largest natural number that divides every natural number of the form (n3–n)(n–2), where n > 2, is 24.