The problem states that three consecutive even integers have a sum of 0. We need to find the value of the greatest of these three integers.

1. Problem Description

The problem states that three consecutive even integers have a sum of

0. We need to find the value of the greatest of these three integers.

2. Solution Steps

Let the three consecutive even integers be $x$, $x+2$, and $x+4$.

The sum of these integers is given as

0. So,

$x + (x+2) + (x+4) = 0$

Combining like terms, we have:

$3x + 6 = 0$

Subtracting 6 from both sides:

$3x = -6$

Dividing both sides by 3:

$x = -2$

Therefore, the three consecutive even integers are -2, -2+2, and -2+4, which are -2, 0, and

2. The greatest integer among these three is

2.

3. Final Answer

2