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 5odd numbers must be integers Only whole numbers can be odd or even; decimals and fractions are neither.
  • odd \(\times\) odd = evenodd \(\times\) 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.

Found in 5 StudyPug lessons

Even and Odd Numbers

Draft Lisa Grade 3 Math placeholder

Learn to identify even and odd numbers using the last digit, pairing objects, and number line patterns, then practice with simple examples.

3rd Grade3rd
Even or Odd Numbers in Number Lines

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Use a number line and skip counting by twos to quickly tell whether a number is even or odd.

1st Grade1st
Even or Odd Numbers of Objects

Grade 1 Math placeholder

Learn to decide whether a group of objects is even or odd by pairing them up and checking for a leftover, with pictures and practice.

1st Grade1st
Grouping Even or Odd Numbers

Grade 1 Math placeholder

See how splitting a group of objects into pairs of two shows right away whether the total is even or odd.

1st Grade1st
How to Tell If a Number Is Even or Odd

Grade 1 Math placeholder

Discover a fast way to identify a number as even or odd by looking at its last digit or by pairing up objects.

1st Grade1st

See also

Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026

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