Åk 6–9

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4.2 Prime and Composite Numbers

Prime Numbers
A whole number can have two or more factors.  Here you have a few examples:

 6: 6, 3, 2, 1 Ex: (6 · 1), (3 · 2) 5: 5, 1 Ex: (5 · 1) 8: 8, 4, 2, 1 Ex: (8 · 1), (2 · 4) 7: 7, 1 Ex: (1 · 7) 12: 12, 6, 4, 3, 2, 1 Ex: (12 · 1), (6 · 2), (3 · 4)

As you can see the number 5 and 7 have only two factors, 1 and themselves. These numbers are called prime numbers

The numbers 6, 8 and 12 have several factors and are called composite numbers.

A prime number is a positive whole number bigger than 1 which cannot be divided into factor other than itself and 1.

Mathematicians struggle to find a formula in order to determine if a certain number is a prime number or not.  An old method is called the sieve of Eratosthene after the Greek philosopher which created the method about 200 year bc.

1. Imagine all the whole numbers starting with 2 on the number line.  The first number on the line is 2 which is a prime number.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2. Then cross out every other number from 2, in other words 4, 6, 8 and so forth.

2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3. The next number which is on the number line is 3. This is the next prime number.

2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4. Cross out each third number. Circle the next number which isn’t crossed out, in other words 5, and cross out each fifth number.

2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Composite Numbers
Those whole numbers which are no prime numbers are called composite numbers. Composite numbers are whole numbers which are divisible by more numbers them themselves and one. 6 is for example divisible by 2 and 3 and therefore is an example of a composite number.

All composite numbers can be divided up into factors of prime numbers, called prime factors. When you do this distribution, it is called prime factorisation:

Ex: What are the prime factors of  72?

The prime factors are: 72 = 2 · 2 · 2 · 3 · 3 = 23 · 32