Use the odd number checker to confirm that an integer is odd and see the remainder of 1 that proves it. It is useful when a rule or a puzzle depends on an odd value and you want certainty, not a guess.
Is this number odd?
Definition of an odd number
An integer n is odd when n = 2k + 1 for some integer k. In words: it is one more than an even number, so halving it always leaves exactly 1 over.
Odd numbers alternate with even numbers on the number line: … −5, −3, −1, 1, 3, 5 …. Two consecutive odd numbers always differ by 2, and an odd number is never divisible by 2, 4, 6 or any other even number.
How to check an odd number
- Type the integer, for instance
2025or-13. - Select Check if Odd or press Enter.
- “Yes, it is odd” comes with the equation n = 2 × k + 1. “No, it is not odd” means the number is even and the remainder is 0.
Negative odd numbers, explained carefully
For −13 the checker writes −13 = 2 × (−7) + 1. Mathematicians choose the remainder to be 0 or 1, so the quotient is rounded down to −7, not −6. You might see −13 % 2 = −1 in a spreadsheet or code. That value is still odd: what matters is that the remainder is not zero.
Worked example: 2,025
2025 divided by 2 equals 1012 with remainder 1.
The last digit is 5, which confirms the result: 2,025 is odd.
Properties of odd numbers
| Rule | Example |
|---|---|
| odd + odd = even | 7 + 9 = 16 |
| odd − odd = even | 15 − 3 = 12 |
| odd × odd = odd | 5 × 7 = 35 |
| odd + even = odd | 7 + 4 = 11 |
| The square of an odd number is odd | 9² = 81 |
| Sum of the first n odd numbers = n² | 1 + 3 + 5 + 7 = 16 = 4² |
To test these rules with your own numbers, try the parity rules explorer on the even and odd numbers guide.
Frequently asked questions
Is 1 an odd number?
Yes. 1 = 2 × 0 + 1. It is the smallest positive odd number.
Is −1 odd?
Yes. −1 = 2 × (−1) + 1, so it leaves remainder 1.
Are all prime numbers odd?
All except 2. Every prime greater than 2 is odd, but many odd numbers, such as 9, 15 and 21, are not prime.
How do I list odd numbers in a range?
Use the Odd Numbers List to list every odd number between two values, or the Odd Number Generator for random ones.