Which statement accurately reflects an even integer?

An even integer is defined as any integer that can be divided by 2 without leaving a remainder. This means that when an even integer is split, it can be grouped into pairs perfectly, with no single unit left over. For example, the number 4 can be paired as (2 and 2) or (1 and 1) twice, demonstrating that it can be evenly divided into groups of two.

This definition aligns precisely with the statement that describes an integer that can be split into pairs without a leftover. In contrast, the idea of an integer being divisible by 3, resulting in a remainder when divided by 2, or being less than zero only, does not encapsulate the properties that define even integers. Thus, the correct statement accurately captures the essence of even integers and is fundamental to understanding the classification of numbers in mathematics.