Prime Numbers and Prime Numbers and Composite Numbers Composite Numbers

Some whole numbers can be divided up Some whole numbers can be divided up evenly, and some can't!evenly, and some can't!

Example: 6 can be divided evenly by 2, or by 3: Example: 6 can be divided evenly by 2, or by 3: 6 = 2 × 3 6 = 2 × 3

or

divided into 2 groups divided into 3 groups

A number that can be divided up evenly is a Composite Number

Example: 7 cannot be divided up evenly:

So 6 is Composite, but 7 is Prime.

A number that can not be divided up evenly is a Prime Number

What is a Prime Number ?What is a Prime Number ?

A Prime Number cannot be divided evenly by any A Prime Number cannot be divided evenly by any number, except 1 or itself.number, except 1 or itself.

Example: is 7 a Prime Number or Composite Number?

We can of course divide 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.

• 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. So 7 is a Prime Number

What is a Composite Number?What is a Composite Number?

A A Composite NumberComposite Number can be divide evenly by numbers can be divide evenly by numbers other than 1 or itself.other than 1 or itself.

Example: is 12 a Prime Number or Composite Number? • You can divide 12 evenly by 1 and 12.

1 × 12 = 12

• You can divide 12 evenly by 2 and 6 (you would get 2 lots of 6 or 6 lots of 2).

2 × 6 = 12

• You can divide 12 evenly by 3 and 4 (you would get 3 lots of 4 or 4 lots of 3).

3 × 4 = 12

We can divide 12 evenly by 1, 2, 3, 4, 6 and 12:

So 12 is also a Composite Number

Important points to remember

• Any whole number greater than 1 is either a Prime number or a Composite number.

• 1 is considered neither a prime number nor a composite number

• 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“.

Examples From 1 to 14Examples From 1 to 14

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

15 A question for you: is 15 Prime or Composite ?

Why All the Fuss about Prime and Why All the Fuss about Prime and Composite?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.

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.”