Year 8 Interactive Maths - Second Edition

## Prime Numbers

A prime number has only two different factors, 1 and itself.

So, 13 is a prime number since it has only two different factors, 1 and 13.

## Composite Numbers

A composite number is a number that has more than two factors.

So, 10 is a composite number as it has more than two factors.
###### Note:

1 is considered neither a prime number nor a composite number as it has 1 factor only.  A prime number has 2 different factors.

#### Example 19

State which of the following numbers are a prime:
a.  6
b.  19

## Prime Factors

Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, …

A prime factor is a factor of a number that is also a prime number.

To express a whole number as a product of prime factors, try prime numbers in order of their magnitude.  That is, first try to find out whether 2 is a factor of the given whole number or not.  If 2 is a factor of the whole number, it will divide into it exactly and we can write the whole number as the product of 2 and another number.  If 2 is a prime, try 2 again to see if we can further write the whole number as a product involving two 2s.  If not, try the next prime, 3, and so on.  Stop when the number has been expressed as the product of prime numbers.

#### Example 20

Express 90 as a product of prime numbers.

##### Solution:

###### Alternative solution:

We can use a factor tree to express 90 as a product of prime numbers.

#### Example 21

Express 200 as a product of prime numbers.