What is an Even Number?
An even number is a whole number (integer) that divides exactly by 2, leaving a remainder of zero. The first few positive even numbers are 2, 4, 6, 8, 10, and 12.
Formally, an even number is any integer of the form n = 2k, where k is also an integer. So 14 is even because 14 = 2 × 7, and −18 is even because −18 = 2 × (−9). Every even number has a partner — the integer it equals when divided by 2.
The opposite of an even number is an odd number, which leaves a remainder of 1 when divided by 2.
Examples of Even Numbers
Even numbers appear in three common forms:
Small positive integers: 2, 4, 6, 8, 10, 12, 14
Larger positive integers: 248, 1,506, 38,792, 100,000
Negative integers: −2, −4, −6, −8, −10, −124
Zero is also even. This often confuses students. The reason is mechanical: 0 = 2 × 0, where 0 is an integer. That fits the definition n = 2k exactly. Zero leaves a remainder of 0 when divided by 2 (because 0 ÷ 2 = 0), which is the test for evenness.
List of Even Numbers from 1 to 100
There are exactly 50 even numbers between 1 and 100.
2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40 |
42 | 44 | 46 | 48 | 50 | 52 | 54 | 56 | 58 | 60 |
62 | 64 | 66 | 68 | 70 | 72 | 74 | 76 | 78 | 80 |
82 | 84 | 86 | 88 | 90 | 92 | 94 | 96 | 98 | 100 |
Table: The 50 even numbers from 1 to 100.
Half of all integers are even, and the other half are odd. So between any 1 and any whole number N, roughly half will be even.
How to Identify an Even Number
Three rules, in order from quickest to most rigorous:
Last-digit rule. If the number ends in 0, 2, 4, 6, or 8, it is even.
Divisibility test. Divide the number by 2. If the remainder is 0, the number is even.
The n = 2k test. If the number can be written as 2 times an integer, it is even.
Worked example — large number: Is 4,328,716 an even number?
The last digit is 6. Since 6 is in the set {0, 2, 4, 6, 8}, the number 4,328,716 is even.
Worked example — tricky case: Is 41,357 even?
The last digit is 7. The digits 4 and 6 appear elsewhere in the number, but only the last digit determines parity. Since 7 is odd, 41,357 is an odd number.
Properties of Even Numbers
When two numbers are combined under addition, subtraction, or multiplication, the result follows a fixed parity rule.
Operation | Even & Even | Even & Odd | Odd & Odd |
|---|---|---|---|
Addition | Even (4 + 6 = 10) | Odd (4 + 5 = 9) | Even (3 + 5 = 8) |
Subtraction | Even (10 − 4 = 6) | Odd (10 − 3 = 7) | Even (9 − 3 = 6) |
Multiplication | Even (4 × 6 = 24) | Even (4 × 5 = 20) | Odd (3 × 5 = 15) |
Table: How the parity of two integers combines under each operation.
Division is not included because dividing two even numbers does not always give an integer (6 ÷ 4 = 1.5, which is neither even nor odd).
Even Numbers vs Odd Numbers
Feature | Even Numbers | Odd Numbers |
|---|---|---|
Divisible by 2 | Yes (remainder 0) | No (remainder 1) |
Last digit | 0, 2, 4, 6, 8 | 1, 3, 5, 7, 9 |
General form | n = 2k | n = 2k + 1 |
Examples | 2, 4, 0, −6 | 1, 3, 7, −5 |
Special Cases
Is 2 an even prime number?
Yes. 2 is the only even prime number.
The reason is mechanical. A prime number has exactly two factors: 1 and itself. Every even number greater than 2 has 2 as a factor, which automatically gives it three or more factors (1, 2, and the number itself). That disqualifies it from being prime. The number 2 escapes this rule because its factors are just 1 and 2 — exactly two factors. So it stays prime.
Are decimals and fractions ever even?
No. Only integers can be classified as even or odd.
The number 1.52 is not even, even though its last digit is 2 — because 1.52 is not an integer. The fraction 1/2 is not even either. (4/2 happens to equal 2, which is even, but that's because 4/2 simplifies to an integer.)
What about negative numbers?
Negative integers can be even or odd. The numbers −2, −4, −6, and −124 are all even. The numbers −1, −3, and −7 are odd. The same rules apply: divisibility by 2 with no remainder.
Parity — The Formal Term
In mathematics, the property of being even or odd is called parity. An even number has parity 0; an odd number has parity 1.
The term shows up in several fields beyond elementary math:
Programming — the modulo operator (
n % 2) returns the parity of nCryptography and computer networks — parity bits detect transmission errors
Combinatorics — parity arguments are used to prove certain results impossible
A parent or older student running into the word "parity" in a textbook or coding tutorial is being told one thing: even or odd.
Even Numbers in the Curriculum
Even and odd numbers first appear in elementary school number sense:
Common Core (US): CCSS 2.OA.3: Grade 2 students determine whether a group of objects has an even or odd number.
NCERT (India): Even and odd numbers appear in Class 3 and are revisited under number patterns and properties in Class 5.
UK National Curriculum (KS1): Year 2 students recognise odd and even numbers.
Common Confusions
"Zero is neither even nor odd." Zero is even — it satisfies n = 2k with k = 0.
"Negative numbers can't be even." They can. −2, −4, −6 are all even.
"Multiples of 2 and even numbers are different." They are the same set.
"If a number contains the digit 4, it is even." Only the last digit matters. 41 is odd.
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