Type a whole number and the even and odd test tells you its parity immediately, together with the division by 2 that proves the answer. It works for zero, for negative numbers and for integers hundreds of digits long.
Even and odd test
What the even and odd test does
The test sorts an integer into one of two groups. Even numbers split into two equal whole halves; odd numbers always leave one left over. Instead of a bare label, the result shows the quotient and remainder, the conclusion, and the last-digit shortcut, so you can check the reasoning yourself or copy it into homework.
Input is read as text, not as a floating-point value, so a 40-digit number keeps every digit and the answer is exact. Anything that is not an integer, such as 2.5, a word, or “Infinity”, gets a clear explanation instead of a wrong label.
How to use the calculator
- Type an integer into the box, for example
128or-45. On a phone, use the ± button to add a minus sign. - Press Check Number or the Enter key.
- Read the result: Even number or Odd number, followed by the division that proves it.
- Use Clear (or Escape inside the box) to start again, or tap an example such as 12, 7, 0 or −5.
The mathematical definition
An integer n is even if there is an integer k with n = 2k. It is odd if there is an integer k with n = 2k + 1. Every integer satisfies exactly one of these.
Equivalently, divide by 2 and look at the remainder: 0 means even and 1 means odd. This is the same as asking whether n is a multiple of 2.
Worked examples
Example 1: 12
12 divided by 2 equals 6 with remainder 0.
Therefore, 12 is even. In the form of the definition, 12 = 2 × 6.
Example 2: 7
7 divided by 2 equals 3 with remainder 1.
Therefore, 7 is odd, because 7 = 2 × 3 + 1.
Example 3: −5
Write −5 = 2 × (−3) + 1. The remainder is 1, so −5 is odd.
Many programming languages report −5 % 2 as −1. That is a convention for truncated division, not a different parity: −1 and 1 differ by 2, so both point to “odd”.
Example 4: 0
0 divided by 2 equals 0 with remainder 0, so 0 is an even number.
Why the last-digit shortcut works
Any integer can be written as 10 × (everything except the last digit) + (last digit). Because 10 = 2 × 5, the first part is always even, so the whole number is even exactly when its last digit is even. That is why 3,456,789,012 is even at a glance, while 1,000,001 is odd.
| Last digit | Parity | Examples |
|---|---|---|
| 0, 2, 4, 6, 8 | Even | 30, 112, −58, 1,004 |
| 1, 3, 5, 7, 9 | Odd | 21, 333, −77, 1,005 |
Common mistakes
- Treating zero as special. Zero is simply even. Read the proof that zero is even.
- Thinking negatives cannot be even. −10 is as even as 10.
- Calling 4.0 or 2.5 even or odd by eye. 4.0 equals the integer 4, so it is even, but 2.5 is not an integer and has no parity.
- Checking the first digit. Only the last digit matters: 9,998 is even.
Frequently asked questions
What is an even and odd test?
It is a check that decides whether an integer is divisible by 2 (even) or leaves a remainder of 1 (odd). This page runs that check and shows the working.
Does the test work for very large numbers?
Yes. Integers of up to 1,000 digits are checked exactly, because the tool never converts them to floating-point numbers that would lose digits.
Why do I get “not an integer” for 3.7?
Even and odd are defined only for whole numbers. 3.7 lies between 3 and 4 and is not a multiple of 2 or one more than a multiple of 2, so it has no parity.
Can I check several numbers at once?
Yes. The Even Odd Calculator checks up to 100 numbers, counts evens and odds, and exports the results as TXT or CSV.
Is my input sent anywhere?
No. With JavaScript enabled, the calculation runs entirely in your browser and nothing is stored.