There is a prime number which is a factor of every sum of three  consecutive integers. What is the number?
I know that any sum of three consecutive integers can be written as n + (n+1) + (n+2), where n is any integer. I also know that this sum can be simplified to 3n + 3, which is always divisible by 3. Therefore, 3 is a prime number that is a factor of every sum of three consecutive integers. 