Example 1

List the first 10 prime numbers.

The first 10 prime numbers are listed in the following chart. Recall prime numbers have exactly two factors, 1 and itself.

Prime Numbers Why?
2
1 × 2
3
1 × 3
5
1 × 5
7
1 × 7
11
1 × 11
13
1 × 13
17
1 × 17
19
1 × 19
23
1 × 23
29
1 × 29

The method shown in Example 2 outlines one way of determining if a number is a prime number. With practice and good reasoning, you will develop strategies that work best for you.

 

Example 2

Show that 11 is a prime number.

Step 1: Try to find a number that divides into 11 evenly (no remainders).

Try the lowest prime number, 2.

11 ÷ 2 =

Try the next lowest prime number, 3.

11 ÷ 3 =

The number 2 is a factor of 4. Since 2 is not a factor of 11, we know that 4 will not be factor of 11 either.


Try the next lowest prime number, 5.
11 ÷ 5

Since half of 11 is 5.5, there is no need to continue beyond 5. There will be no factors between 6 and 11 if there aren't any between 1 and 5.

 

Step 2: Try dividing by the number itself.

Since the number 11 can only be divided evenly by 1 and itself, the number 11 is a prime number.