Subject: Integers
Name: Jimmy
Who are you: Student

Basically i want to know how you prove that the product of any 3 consecutive integers is a multiple of 6


Hi Jimmy.

If you count by threes (3, 6, 9, 12, etc.) you see that any three consecutive integers has to have one of these numbers, so it has at least one number that is divisible by 3. As well, any three consecutive integers has at least one even number (which is divisible by 2). So when you multiply any three consecutive integers, the product has 3 and 2 as factors.

Stephen La Rocque.>