Even and Odd
A number is even if it divides by 2 with no remainder.
Formula
Variables
Example
8 is even, 7 is odd
How it works
A whole number is even when it can be split into two equal groups with nothing left over, which is exactly what happens when dividing by 2 gives remainder 0. In modular arithmetic, this is written as n mod 2 = 0, meaning the number’s leftover after dividing by 2 is zero. If the remainder is 1 instead, the number is odd. This idea works because every whole number must be either one more than a multiple of 2 or exactly a multiple of 2.
When to use it
Use this when you need to check whether a number is divisible by 2, such as in counting problems, patterns, or deciding if something can be paired up evenly. It is also useful in algebra, programming, and number theory when separating even and odd cases.
Worked example, step by step
Check whether 14 is even or odd. 14 ÷ 2 = 7 Remainder = 0 14 mod 2 = 0 Therefore, 14 is even.
Common mistakes to avoid
- Thinking a number is even just because it ends in 0 or 2 without checking other digits carefully
- Mixing up quotient and remainder when using division
- Assuming negative numbers cannot be even or odd
Did You Know?
Whether a number is even or odd is called its "parity" — a concept that powers error-detecting codes in every computer.
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