Question 969707: Prove that the product of three consecutive positive integers
is divisible by 6.
Answer by CubeyThePenguin(3113)   (Show Source):
You can put this solution on YOUR website! n(n+1)(n+2)
Out of these numbers, at least one of them is even and at least one of them is a multiple of 3.
even:
even, odd, even
odd, even, odd
divisible by 3 (use remainders):
0, 1, 2
1, 2, 0
2, 0, 1
Therefore, the product of any three consecutive integers is divisible by 6.
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