even number
B1Academic, Technical, Everyday
Definition
Meaning
An integer that is exactly divisible by two.
Any whole number ending in 0, 2, 4, 6, or 8, or more formally, any integer n where n = 2k for some integer k.
Linguistics
Semantic Notes
A purely mathematical concept. Its opposite is 'odd number'. The property of being 'even' is a fundamental classification in arithmetic.
Dialectal Variation
British vs American Usage
Differences
No significant differences in definition or usage. The concept is identical in all English-speaking mathematical traditions.
Connotations
Neutral, mathematical.
Frequency
Equally common in all contexts involving basic mathematics.
Vocabulary
Collocations
Grammar
Valency Patterns
N is an even numberThe set of even numbersEven numbers have the property that...Numbers like 2, 4, and 6 are even.Vocabulary
Synonyms
Neutral
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “On an even keel (idiomatically related to stability, not directly to numbers)”
Usage
Context Usage
Business
Rare, except in basic data analysis or partitioning (e.g., 'split the group into even and odd numbered teams').
Academic
Very common in mathematics, computer science, and logic education.
Everyday
Common when discussing basic arithmetic, house numbers, or simple grouping.
Technical
Fundamental in mathematics, programming (e.g., checking n % 2 == 0), and digital logic.
Examples
By Part of Speech
adjective
British English
- The even-numbered houses are on the south side of the street.
- Please select an even integer for the calculation.
American English
- The even-numbered pages contain the exercises.
- Make sure the sample size is an even number.
Examples
By CEFR Level
- Two, four, six, and eight are even numbers.
- My house number is an even number: 12.
- To check if a number is even, see if it ends in 0, 2, 4, 6, or 8.
- The sum of two even numbers is always even.
- In the algorithm, we iterate through the even-numbered indices first.
- The property of being an even number is preserved under addition.
- The set of all even numbers forms an ideal in the ring of integers.
- Parity checking, which determines if a number is even or odd, is fundamental in error detection codes.
Learning
Memory Aids
Mnemonic
Think of 'even' as meaning 'balanced' or 'paired'. An even number can always be split into two equal whole-number groups, like partners in a dance.
Conceptual Metaphor
STABILITY AND BALANCE (Even numbers are seen as balanced, complete, and symmetrical, unlike 'odd' numbers which are perceived as unbalanced or with a remainder).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Direct translation is straightforward: 'чётное число'. No significant trap, but note the spelling and pronunciation of 'even' /ˈiːvən/.
Common Mistakes
- Confusing 'even' with 'equal' (e.g., 'The teams have even numbers of players' vs. 'The number 4 is even').
- Pronouncing 'even' as /ˈiːvɛn/ (should be /ˈiːvən/).
- Writing 'even number' as one word ('evennumber').
Practice
Quiz
Which of the following is a defining property of an even number 'n'?
FAQ
Frequently Asked Questions
Yes, zero is an even number because it is divisible by 2 (0 ÷ 2 = 0, an integer with no remainder).
Yes. Evenness is a property of all integers. -2, -4, -6 etc. are even numbers because they can be expressed as 2 multiplied by an integer (e.g., -2 = 2 * -1).
The opposite is an 'odd number' (or less commonly, 'uneven number'), which is an integer not divisible by two.
It's a fundamental concept in arithmetic and number theory, essential for understanding divisibility, patterns in numbers, and forming the basis for more complex ideas in mathematics and computer science (like parity bits and modular arithmetic).