the number n(n²-1) is divisible by(highest number)

the answer is 6 .

proof : the given qty = (n-1)n (n+1) = product of three consecutive integers . Which must be divisible by 3!=6 ( a theorem from number theory)

Just for reference and no work i am proving that 3 consecutive numbers are divisible by 6.

Let the three numbers are n(n+1)(n+2)

 P₁=1*2*3=6(True)

Let us assume that P_k=k(k+1)(k+2) is true

P_k+1=(k+1)(k+2)(k+3)

=k(k+1)(k+2)+3(k+1)(k+2)

=6N+3*2R

=6(N+R)

=6m

So three consecutive numbers are sivisible by 6 or 3! .

that is true only if n is odd. But it is always divisible by 6. So, 6 should be right answer.