Even

Even refers to the property of numbers that are divisible by two. In mathematics, an even integer is any integer n for which there exists another integer k with n = 2k. By definition, zero is even, as are 2, -4, 8, and so on. The term contrasts with odd integers, which are not divisible by 2.

Parity classifies all integers into two sets: even and odd. Parity is closed under addition and subtraction: the sum or difference of two even numbers is even, and the sum of two odd numbers is even. The sum of an even and an odd number is odd. The product of two integers is even if at least one factor is even; the product of an even and any integer is even. Dividing an even number by 2 yields another integer, which may be even or odd.

In modular arithmetic, even numbers are precisely those congruent to 0 modulo 2. In computing and digital systems, parity checks and even/odd classifications are used for simple error detection and data validation.

The term “even” can also describe phenomena that are balanced or uniformly distributed in a general sense, but in formal mathematics it specifically denotes divisibility by two when applied to integers.