Even Number

Even Number

An integer that is a multiple of 2. The even numbers are { . . . , –4, –2, 0, 2, 4, 6, . . . }.

See also

Key Formula

n = 2k

Where:

$n$ = the even number
$k$ = any integer

Worked Example

Problem: Determine whether 14 is an even number.

Step 1: Divide the number by 2.

14 \div 2 = 7

Step 2: Check whether the result is an integer with no remainder. Since 7 is an integer and the remainder is 0, the number is even. Equivalently, we can write 14 = 2 × 7, which matches the form n = 2k.

14 = 2 \times 7

Answer: Yes, 14 is an even number because it is a multiple of 2.

Why It Matters

Even and odd numbers are foundational in number theory and appear throughout algebra. Recognizing whether a number is even helps you simplify fractions, factor expressions, and predict patterns — for instance, the sum of two even numbers is always even, and the product of any integer with an even number is always even.

Common Mistakes

Mistake: Thinking 0 is not an even number.

Correction: Zero is even because 0 = 2 × 0, which fits the definition of a multiple of 2. It divides by 2 with no remainder.

Related Terms

Odd Number — An integer that is not divisible by 2
Integers — The set of numbers that can be even or odd
Divisibility — Even numbers are defined by divisibility by 2
Multiple — Even numbers are multiples of 2