Multiple Choice Question (MCQ)
The product of three consecutive integers is divisible by

×
5

✓
6

×
7

×
8
The product of three consecutive integers is divisible by
5
6
7
8
Let the three consecutive numbers be 3n1, 3n,3n+1
Then the product of the three numbers will be
(3n1)\cdot3n\cdot (3n+1)
=3n(9n^21)
Obviously 3n(9n^21) is divisible by 3 and it's also an even number. Why?
if n is an even number, our claim is true.
If n is an odd number, then n^2 is also an odd number. 9 is odd. The product of two odd numbers is still an odd number. However, if subtract 1 from the odd number, then the difference is even.
So in both cases, 3n(9n^21) is even.
Therefore, the product of three consecutive integers is divisible by 6.