Even Numbers

High School

Definition

Even numbers are integers that are divisible by 2. In other words, they are multiples of 2. Some of the examples are - 6, - 4, - 2, 0, 2, 4, 6.

Worked examples

\(2, 4, 6, 8, 10\)

Each number divides evenly by 2 with no remainder.

\(-6 \div 2 = -3 \quad \)and\( \quad 0 \div 2 = 0\)

Negative integers and zero can be even too — if 2 divides it evenly, it's even.

\(2n = 2(5) = 10\)

Any integer times 2 produces an even number; here \(n=5\) gives 10.

Common mistakes

\(0\) is not even → \(0\) is even because \(0 \div 2 = 0\) Zero is divisible by 2 with no remainder, so it is even.
Negative numbers like \(-4\) cannot be even → \(-4\) is even because \(-4 \div 2 = -2\) Even and odd apply to all integers, positive and negative.
\(2.5\) is even because it has a 2 → Only integers can be even; \(2.5\) is not an integer Even numbers must be whole numbers (integers); decimals and fractions are neither even nor odd.

Where you'll use it next

You'll use even numbers when learning odd numbers, divisibility rules, factoring, and parity arguments in number theory. They also appear in patterns, sequences, and modular arithmetic in algebra.