Prime Numbers and Composite Numbers

A Prime Number can be divided evenly only by 1, or itself.

Some 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:

Not into groups of 1

OK, we could have divided 7 into seven 1s like this:

7 = 1 x 7

But we could do that for any whole number, so we should also say that we are not interested in dividing by 1, or by the number itself, and so we say it like this:

Example: is 7 a Prime Number?

• You cannot divide 7 evenly by 2 (you would get 3 and 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

Sometimes a number can be divided evenly lots of ways:

And note this:

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.

Examples From 1 to 14

I have shown in bold any factors other than 1 or the number itself:

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.

And that is why they are called "Composite" numbers because Composite means "something made by combining things"

There are many puzzles in mathematics that can be solved more easily when you "break up" the Composite Numbers into their Prime Number factors.