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Prime and Composite Numbers


 

What are Prime Numbers?

Prime Numbers are numbers which can only be divided by number 1 and that number itself. 

 

 

Rule:

 

Prime Numbers always have only 2 factors.

 

They are;

Number 1 

 

AND

 

The number itself

 

 

Explanation:

 

 

Step 1:

 

What are the factors of 2?

 

1 x 2 = 2

 

2 x 1 = 2

 

 

 

The factors of 2 are number 1 and 2 itself. Therefore 2 is a Prime Number.

 

 

Step 2:

 

What are the factors of 4?

 

1 x 4 = 4

 

4 x 1 = 4

 

2 x 2 = 4

 

 

 

 

The factors of 4 are number 1 , 2  and itself. 4 has three factors. 

 

Therefore 4 is not a ‘Prime Number’, it is a ‘Composite Number’.

 

 

 

Finding the Prime Numbers in the first 20 numbers

 

 

Number

Factors

1

1

2

1 , 2

3

1 , 3

4

1 , 2, 4

5

1 , 5

6

1 , 2, 3 , 6

7

1 , 7

8

1 , 2 , 4 , 8 

1 , 2 , 3 , 9 

10

1 , 2 , 5 , 10 

11 

1 , 11

12

1 , 2 , 3 , 4 , 6 , 12

13

1 , 13 

14 

1 , 2 , 7 , 14 

15 

1 , 3 , 5 , 15 

16

1 , 2 , 4 , 8 , 16

17

1 , 17

18

1 , 2 , 3 , 6 , 9 , 18  

19 

1 , 19 

20 

1 , 2 , 4 , 5 , 10 , 20

 

What are the numbers that have only two factors in the above table?

 

2 , 3 , 5 , 7 , 11 , 13 , 17, 19

 

You can clearly see in the table, that these numbers have only 2 factors.

 

 

They are always;

Number 1 

 

AND

 

 The number itself

 

 

Therefore such numbers are called ‘Prime Numbers’.

 

 

All the other numbers in the table have more than two factors, except number 1.

 

 

Therefore numbers with more than two factors are called ‘Composite Numbers’.

 

 

Then what about number 1? Is it Prime or Composite?

 

* 1 has only one factor which is 1. Therefore it is neither Prime nor Composite.