2015 · Q5
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
Elementary MathematicsNumber System
- A6
- B12
- C24
- D48
Explanation
(n^3 - n)(n - 2) = (n - 1)n(n + 1)(n - 2), the product of four consecutive integers, so it is always divisible by 4! = 24. For n = 3 the value is exactly 24, so no larger number can divide every such value. Hence option (c).