Odd number

High School

Definition

An integer that cannot be factored by 2. Any number containing 1,3,5,7,9 in the ones place is a odd number. Some odd number examples include: 11, 23, 55, 67, 89, 111. Odd numbers go by the pattern 1+2X, with X being any integer.

Worked examples

\(7, 15, 23, 101\)

Each number has 1, 3, 5, 7, or 9 in the ones place and cannot be divided evenly by 2.

\(1 + 2(4) = 9\)

Using the pattern \(1 + 2X\) with \(X = 4\) gives the odd number 9.

Common mistakes

\(0\) is odd → \(0\) is even Zero is divisible by 2, so it is even. Odd numbers leave a remainder of 1 when divided by 2.
\(2.5\) is odd because it ends in 5 → odd numbers must be integers Only whole numbers can be odd or even; decimals and fractions are neither.
odd \(\times\) odd = even → odd \(\times\) odd = odd The product of two odd numbers is always odd, e.g., \(3 \times 5 = 15\).

Where you'll use it next

You'll use odd and even numbers when studying divisibility rules, integer properties, patterns in sequences, and modular arithmetic. They also appear in proofs and problem-solving across algebra and number theory.