Prime and Composite Numbers

Prime Numbers have only 1 and themselves as factors, examples are 7,11, 13. Numbers that are not prime are composite numbers and can be expressed as a product of prime numbers. e.g 6 = 2 X 3
Prouct tree for 12
12 < 6
2
6 < 2
3 So the numbers at the tips of the branches are all prime so 12 = 2 X 3 X 2
Lets try another one 60 < 4 < 2
2

15 < 5
3
So 60 = 2 * 2 * 3 * 5.
Highest Common Factor
Suppose we have two numbers 70 and 99
Express each as prime factors we have 70 = 2 X 5X 7 and 99 = 3X3 X 11
We see there are no common factors except 1, so these numbers are relatively prime, they are prime in relation to one another.
Now Consider 18 and 30
18 can be written as 2 X 3 X 3 and 30 = 2 X 3 X 5
The common factors are 2 and 3 and 6. The highest common factor is 6. So to get the HCF(Highest Common Factor) we express each number as a product of prime factors and then multiplying togethers all the factors which the prime factors have in common. Another way of saying this is find the largest number that divides into both. 6 is the largest number that divides inot 18 and 30.