Year 8 Interactive Maths - Second Edition

Prime Numbers

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

Solution:

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.

Solution:

Key Terms

prime number, composite number, prime factor, product of prime factors, factor tree