Prime Numbers and Composite Numbers
A Prime Number can be
divided evenly only by 1, or itself.
Prime or Composite?
Any whole number greater than 1 is either prime or composite:
A Prime Number can be
divided evenly only by 1, or itself.
Example: 7 cannot be divided evenly any other way except into 7 ones:
You cannot divide it evenly into 2 (you would get 3 and 3, with one left over)
Nor can you divide it evenly by 3 (you would get 3 lots of 2, with one left over)
Nor can you divide it evenly by 4 or 5 or 6.
But you could have one group of 7, or seven groups of 1.
So 7 can only be divided evenly by 1 or itself (7):
7 = 1 × 7
So 7 is a Prime Number
A Composite Number can
be divided evenly by numbers other than 1 or itself.
Example: 6 can be divided evenly by 2, or by 3 (as well as by 1 or 6):
6 = 1 × 6
6 = 2 × 3
Like this:
 |
or |
 |
| divided into 2 groups |
|
divided into 3 groups |
So 6 is a Composite Number
Sometimes a number can be divided evenly lots of 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 a Composite Number
Factors
"Factors" are the numbers you multiply together to get
another number:
So if you find that the only factors of a number are 1 and the number, then it is prime.
| 2 = 1 × 2 |
Prime |
| 3 = 1 × 3 |
Prime |
| 4 = 1 × 4 or 4 = 2 × 2 |
Composite |
Examples From 1 to 14
I have shown in bold 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?
 |
Well, 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 can be broken into 2, 2 and 3:
12 = 2 × 2 × 3
(Yes, 2 is mentioned twice. Because I broke 4 into its prime numbers of 2 and 2).
And 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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