An odd or unpaired number is an integer that is not even, so it can not be divisible by 2. An odd number of objects can thus not be divided into two equal parts. The odd numbers are ... -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, ....
All prime numbers, except 2, are necessarily odd (because otherwise divisible by 2 and thus no prime).
The sum of two odd numbers is an even number, for example 159 + 73 = 232. The product of two odd numbers is again odd, for example 13 × 21 = 273. Therefore, the odd numbers are not closed for the addition, but for multiplication.
The sum of an odd and even number is odd again, for example 55 + 128 = 183. The product of an odd and even number is equal: 9 × 12 = 108.
The set of odd numbers has a neutral element for multiplication, namely the number 1. The set of even numbers does not have a neutral element for the multiplication. The odd numbers have no neutral element for the addition. The set of even numbers, however, is the number 0.
In the usual decimal mode, an odd number as the last digit has 1, 3, 5, 7 or 9. Also see
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