Prime Numbers and Composite Numbers
A Prime Number can be
divided evenly only by 1, or itself.
Some whole numbers can be divided up evenly, and some can't!
Example:
6 can be divided evenly by 2, or by 3:
6 = 2 × 3
Like this:
 |
or |
 |
divided into 2 groups |
|
divided into 3 groups |
But 7 cannot be divided up evenly:
And we give them names:
- When a number can be divided up evenly it is a Composite Number
- When a number can not be divided up evenly it is a Prime Number
So 6 is Composite, but 7 is Prime.
And that explains it ... but I have some some more details to mention ...
Not Into Groups of 1
OK, we could have divided 7 into seven 1s (or one 7) like this:
 |
7 = 1 x 7 |
But we could do that for any whole number!
So we should also say we are not interested in dividing by 1, or by the number itself.
Definitions
A Prime Number cannot be divided evenly by any number
(except 1 or itself).
Example: is 7 a Prime Number or Composite Number?
- You cannot divide 7 evenly by 2 (you would get 2 lots of 3, with one left over)
- You cannot divide 7 evenly by 3 (you would get 3 lots of 2, with one left over)
- You cannot divide 7 evenly by 4, or 5, or 6.
You can only divide 7 into one group of 7 (or seven groups of 1):
|
7 = 1 x 7 |
So 7 can only be divided evenly by 1 or itself (7):
So 7 is a Prime Number
And also:
A Composite Number can be divided evenly
by numbers other than 1 or itself.
Like this:
Example: is 6 a Prime Number or Composite Number?
6 can be divided evenly by 2, or by 3, as well as by 1 or 6:
6 = 1 × 6
6 = 2 × 3
So 6 is a Composite Number
Sometimes a number can be divided evenly many ways:
Example: 12 can be divided evenly by 1, 2, 3, 4, 6 and 12:
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
So 12 is also a Composite Number
And note this:
Any whole number greater than 1 is either Prime or Composite
Factors
You can make the same definitions using Factors.
"Factors" are the numbers you multiply
together
to get
another number.
So here is just a different way of saying the same thing from above:
When the only factors of a number are 1 and the number,
then it is a Prime Number
And remember this is only about Whole Numbers (1, 2, 3, ... etc), not fractions or negative numbers. So don't say "I could multiply ½ times 6 to get 3" OK?
Examples:
3 = 1 × 3
(the only factors are 1 and 3) |
Prime |
| |
|
6 = 1 × 6 or 6 = 2 × 3
(the factors are 1,2,3 and 6) |
Composite |
Examples From 1 to 14
I have highlighted any factors other than 1 or the number itself:
Number |
Can be Evenly
Divided By |
Prime, or
Composite? |
1 |
(1 is not considered prime or composite) |
2 |
1, 2 |
Prime |
3 |
1, 3 |
Prime |
4 |
1, 2, 4 |
Composite |
5 |
1, 5 |
Prime |
6 |
1, 2, 3, 6 |
Composite |
7 |
1, 7 |
Prime |
8 |
1, 2, 4, 8 |
Composite |
9 |
1, 3, 9 |
Composite |
10 |
1, 2, 5, 10 |
Composite |
11 |
1, 11 |
Prime |
12 |
1, 2, 3, 4, 6, 12 |
Composite |
13 |
1, 13 |
Prime |
14 |
1, 2, 7, 14 |
Composite |
... |
... |
... |
So when there are more factors than 1 or the number itself, the number is Composite.
A question for you: is 15 Prime or Composite?
Why All the Fuss about Prime and Composite?
Because you can "break apart" Composite Numbers into Prime Number factors.
 |
It is like the Prime Numbers are the basic building blocks of all numbers.
And the Composite Numbers are made up of Prime Numbers multiplied together. |
Example: 12 is made by multiplying the prime numbers 2, 2 and 3 together.
12 = 2 × 2 × 3
The number 2 was repeated, which is OK. In fact you would probably write it like this:
12 = 22 × 3
And that is why they are called "Composite" Numbers because composite means "something made by combining things"
This idea is so important it is called The Fundamental Theorem of Arithmetic.
There are many puzzles in mathematics that can be solved more easily when you "break up" the Composite Numbers into their Prime Number factors.
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