Prove: The product of any three consecutive integers is divisible by $6$. I'm new to number theory and was wondering if someone could help me with this proof. 
Prove: The product of any three consecutive integers is divisible by $6$. 
So far I have $\cfrac{x(x+1)(x+2)}{6}$; How would I go about proving this? Should I replace $x$ with $k$ and then $k$ with $k+1$ and see if the statement is true?

Of $n$, $n +1$, $n +2$, one must be even, so divisible by 2 (why?). One must be divisible by 3 (why?). So their product must be divisible by $2 \times 3$ (why?) ...
