Even, Odd, Composite and Prime Numbers
In mathematics, numbers have different characteristics and relationships. Natural numbers are the
set of counting numbers (1, 2, 3 . . .). We can group or identify natural numbers in different ways.
Even & Odd Numbers
One way we can group natural numbers is to identify them as even and odd numbers. How do
we know when a number is even or odd? Let’s look at the rules below.
THE RULES
Even
Odd
or
?
___________________________________________

Has 2 as a factor and is divisible by 2

Does not have 2 as a factor

Is the sum of 2 even numbers

Not divisible by 2

Is the sum of 2 odd numbers

Is the sum of an even and odd number

Has an even number or zero as ones place

Has an odd number in the ones place
When we draw a picture, we see that even numbers always have a partner. Odd numbers do not.
2
even
3
odd
?
6
even
7
odd
?
PRACTICE!
Using manipulatives, pictures, and words, show why the following numbers are even or odd.
1. 97
2. 1001
3. 5,318
Even, Odd, Composite and Prime Numbers
Another way we can group or identify natural numbers is by identifying them as being composite
or prime.
Composite Numbers
A composite number is a natural number that has more than two different factors. Some
examples of composite numbers are 4, 8, 9, 12, and 20. Each of these numbers has more than
two factors.
Look at the factor trees below. The number 4 is a composite number because its factors are 1,
2, and 4. The number 8 is a composite number because its factors are 1, 2, 4, and 8. Notice
factors are in bold faced type.
8
4
2
2 1
2
2
2
2
1
4
1
2
2
2
1 2
1
We can also determine if a number is a composite number by drawing an array, or a rectangular
drawing of a number.
4
factors 4 x 1
8
factors 2 x 2
12
factors 12 x 1
factors 4 x 3
factors 6 x 2
factors 8 x 1
factors 4 x 2
20
factors 20 x 1
factors 10 x 2
factors 5 x 4
Even, Odd, Composite and Prime Numbers
If we can represent a number with an array other than the number x 1, then the number is a
composite number. Look back at the factor trees for composite numbers. We can see that all
the composite numbers can be represented in at least 2 ways.
PRACTICE!
1. Name 5 composite numbers not yet identified on the page.
Prime Numbers
A prime number is a natural number that has exactly two different factors: 1 and the number
itself. For example, the numbers 2, 3, 5, and 7 are prime numbers. The only numbers that will
divide into a prime number evenly are one and the number itself. Like composite numbers, a
prime number can also be determined by drawing a factor tree. Factors are in bold type.
2
2
3
1
3
5
1
5
7
1
7
1
A prime number can also be determined by drawing an array, or a rectangular drawing of a
number.
2
factors – 2 x 1
3
factors – 3 x 1
5
factors – 5 x1
7
factors – 7 x 1
Notice that each of the prime numbers above has only two factors – 1 and the number itself.
The number 1 is neither prime nor composite – it only has one factor – itself.
PRACTICE!
1. Name 5 prime numbers not yet identified on this page.