Final answer:
The product of any three consecutive natural numbers is divisible by 6 because among three consecutive numbers, there will always be at least one even number and one multiple of 3, providing the factors necessary for divisibility by 6.
Step-by-step explanation:
To demonstrate whether the product of any three consecutive natural numbers is divisible by 6, we can use a simple proof by example. Let's consider three consecutive natural numbers: n, n+1, and n+2. Among these three numbers, at least one number is even, which means it is divisible by 2. Furthermore, at least one of these numbers is divisible by 3, because any set of three consecutive numbers will include a multiple of 3 (since every third number is divisible by 3).
Therefore, we have at least one factor of 2 and one factor of 3 in the product of any three consecutive numbers, which means the product is divisible by 2 × 3 = 6. Hence, the statement is proven.