The largest natural number which divides every natural number of the form n3 ndash n n ndash 2 where...........

Quantitative Aptitude (CDS) Number System

The largest natural number which divides every natural number of the form (n³ – n) (n – 2), where n is a natural number greater than 2 is

(n³ - n) (n-2) = n(n²- 1)(n - 2)

= n ( n - 1)(n + 1)(n - 2)

As n > 2 (natural number) , Putting n = 3

(n - 2)(n - 1)n(n + 1) = (3 - 2 )( 3 - 2 )( 3 - 1 ) 3(( 3 + 1) = 1 $\times$ 2 $\times$ 3 $\times$ 4 = 24

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