Even

Even is a term used in mathematics and statistics to describe a number that is divisible by 2. In the context of mathematics, an even number is an integer of the form n = 2k, where k is an integer. The set of even numbers is denoted by 2Z or 2ℤ.

Definition

An integer n is even if there exists an integer k such that n = 2k. This definition can be written in the formal language of set theory as: n ∈ Z is even if and only if there exists k ∈ Z such that n = 2k.

Properties

Even numbers have several properties that distinguish them from odd numbers. Some of these properties include:

• The sum of two even numbers is always even.
• The product of two even numbers is always even.
• The difference between two even numbers can be even or odd.
• The division of two even numbers can be even or odd, or not an integer.

Examples

Examples of even numbers include −4, 0, 2, 10, and 100. Note that zero is considered an even number because it can be written as 2 × 0.

See also

• Odd number
• Integer
• Number theory
• Parity

References

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