Even and Odd Numbers

Every whole number is either even or odd. An even number can be split into two equal groups with nothing left over, like 6 shared into two groups of 3. An odd number always has one item left over when it is split into groups of two, like 7 sharing into three pairs plus a single leftover item.

This idea of grouping into twos is the easiest way to picture the difference before moving on to a quicker rule based on digits.

Look at the two groups of dots below. The group of 6 dots splits perfectly into 3 pairs. The group of 7 dots also makes 3 pairs, but one dot is left without a partner.

Pairing objects works well for small numbers, but it gets slow for large ones. Instead, look only at the last digit of the number:

• If the last digit is 0, 2, 4, 6, or 8, the number is even.
• If the last digit is 1, 3, 5, 7, or 9, the number is odd.

For example, 84 ends in 4, so 84 is even. The number 137 ends in 7, so 137 is odd. This rule works no matter how many digits the number has, because only the ones place decides whether the number can be split evenly into twos.

Even and odd numbers alternate every time you count by one. Starting at 0 and counting up, the pattern goes even, odd, even, odd, and so on.

This alternating pattern is closely related to skip counting. Practicing counting patterns such as adding with patterns up to 100 makes it much easier to spot even and odd numbers quickly.

Once a number is classified, it helps to know what happens when even and odd numbers are combined by addition:

First number	Second number	Result
Even	Even	Even
Odd	Odd	Even
Even	Odd	Odd

For example, \( 6 + 8 = 14 \) (even plus even gives even), \( 5 + 7 = 12 \) (odd plus odd gives even), and \( 4 + 9 = 13 \) (even plus odd gives odd). Recognizing this shortcut is useful when working through mixed patterns that combine several counting rules at once.

Classify each number as even or odd: 23, 40, 57, 68.

• 23 ends in 3, so 23 is odd.
• 40 ends in 0, so 40 is even.
• 57 ends in 7, so 57 is odd.
• 68 ends in 8, so 68 is even.

Being able to sort numbers this quickly is a useful skill when solving word problems involving patterns, where identifying even or odd totals can confirm whether an answer makes sense.

Related lessons

• Math 2