Which one of the following is the greatest number by which the product of three consecutive even numbers would be exactly divisible ?

To find the greatest number that exactly divides the product of three consecutive even numbers, we represent them as 2n, 2n+2, and 2n+4. Each of these three numbers is divisible by 2, contributing a factor of 2^3 = 8 . Furthermore, in any sequence of two consecutive even numbers, one must be a multiple of 4, providing an additional factor of 2 . Thus, the product is always divisible by 2^4 = 16. Additionally, among any three consecutive integers (n, n+1, n+2), one must be divisible by 3 . Since the sequence of even numbers corresponds to 2(n), 2(n+1), and 2(n+2), the product must also contain a factor of 3 . Combining these factors, the product is always divisible by 16 * 3 = 48 . Testing the smallest case (2, 4, 6) gives 2 * 4 * 6 = 48, confirming 48 is the greatest such divisor.