PROVE THAT THE PRODUCT OF THREE CONSECUTIVE POSITIVE INTEGER IS DIVISIBLE BY 6.

The trick to solve this question is to first apply Euclid's division lemma. From that you will obtain that any positive integer is of the form 6q, 6q+1, 6q+2, 6q+3, 6q+4 or 6q+5.

 

Now, one by one take n equal to above expressions and then prove that product of three consecutive integers is divisible by 6.

Or in other words prove that n(n+1)(n+2) = 6m where m is an integer.