# Highest Common Factor (HCF)

Given any number, its factors are numbers which can divide it and the solution is a whole number. For example: What are the factors of 10? To answer this, 10 is divided by all numbers between 1 and 10.

10 ÷ 1 = 10                  10 ÷ 6 = 1.67
10 ÷ 2 = 5                    10 ÷ 7 = 1.43
10 ÷ 3 = 3.33               10 ÷ 8 = 1.25
10 ÷ 4 = 2.5                 10 ÷ 9 = 1.11
10 ÷ 5 = 2                    10 ÷ 10 = 1
Therefore, the factors of 10 = 1, 2, 5 and 10

Using this approach, the factors of 6 will be 1, 2, 3 and 6; because if 6 is divided by 4 and 5, the answers will not be whole numbers. That is to say the common factors of 10 and 6 are 1 and 2. And the Highest Common Factor (HCF) of 10 and 6 is 2. But the following should be noted:

a) 1 is a factor of any number
b) All numbers are factors of themselves
c) The factor of a number CANNOT be greater than the number itself.

Another example. What is the HCF of 12 and 15?
Factors of 12 = 1, 2, 3, 4, 6 and 12
Factors of 15 = 1, 3, 5 and 15
Common factors of 12 and 15 = 1 and 3
HCF of 12 and 15 = 3