Yes, an even integer is always divisible by 2. This is the fundamental definition of an even number.
Understanding Even Numbers
An even number is defined as any integer that is divisible by 2 without leaving a remainder. This means that when you divide an even number by 2, the result is another whole number.
-
Examples of Even Numbers: 2, 4, 6, 8, 10, -2, -4, -6, etc. All these numbers are perfectly divisible by 2.
-
Mathematical Representation: An even integer can be expressed as 2 * n, where 'n' is any integer (including negative integers). This directly shows its divisibility by 2.
Proof and Further Insights
As noted in several sources (Reddit, GMAT Club, Quora), the concept of even and odd numbers is intrinsically linked to divisibility by 2. If a number is divisible by 2, it's even; otherwise, it's odd. This applies to both positive and negative integers.
The statement "Even numbers are divisible by 2" is a foundational concept in number theory and is not something that requires extensive proof; it's a definition.
Conclusion
The divisibility of even integers by 2 is a core principle of arithmetic. There's no exception to this rule.
