evennumbers

An even number is an integer that is divisible by two without leaving a remainder. This means that an even number can be expressed in the form 2k, where k is any integer. For example, 0, 2, 4, 6, 8, and 10 are all even numbers, as are their negative counterparts -2, -4, -6, and so on.

The most straightforward way to determine if a number is even is to check its last digit. If the last digit of an integer is 0, 2, 4, 6, or 8, then the number is even. Conversely, if the last digit is 1, 3, 5, 7, or 9, the number is odd. This rule applies to all integers, regardless of their size.

Even numbers play a fundamental role in mathematics. They are used in concepts like prime factorization, modular arithmetic, and number theory. For instance, when discussing prime numbers, it is known that 2 is the only even prime number, as all other even numbers greater than 2 are divisible by 2 and therefore not prime. The concept of parity, which categorizes numbers as either even or odd, is a foundational element in many mathematical proofs and algorithms.