Counting numbers greater than 1 are either prime numbers or composite numbers. 

  A prime number is a counting number greater than 1 whole only factors are 1 and the number itself.

  A composite number is a counting number that has three or more    factors.

Example1:  Make a list of the prime numbers less than 20.

Solution:  

Step 1:  List the counting numbers from 1 to 20.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Step 2:  Decide which numbers are not prime.

  1 is not prime

  2 is the first prime number

  All the even numbers greater than 2 are divisible by 2 so they are not prime numbers

               The numbers that are left are 2, 3, 5, 7, 9, 11, 13, 15, 17, 19

  The numbers 9 and 15 are divisible by 3 so they are not prime.

  The numbers 2, 3, 5, 7, 11, 13, 17, and 19 are only divisible by 1 and the number itself so these are the prime numbers less than 20.

Example 2:  List the composite numbers between 30 and 40.

Solution:  

Step 1:  Write all the counting numbers between 30 and 40.

                                 31, 32, 33, 34, 35, 36, 37, 38, 39

Step 2:  Decide which numbers are composite.

  All the even numbers are divisible by two so 32, 34, 36 and 38 are composite.

  33, 36, and 39 are divisible by 3 so they are composite.

  35 is divisible by 5 so it is composite.

  Since 31 and 37 are prime, the list of composite numbers between 30 and 40 is 32, 33, 34, 35, 36, 38, and 39.

Remember:  

1.  Prime numbers have only two factors.

2.  Composite numbers have more than two factors.

3.  The number 1 is not prime or composite because it has only one factor.

Let's Practice!