Objectives:
At the end of this lesson, students should be able to;
The highest common factor which is also known as the greatest common factor is the biggest or largest factor that is common to a set of numbers.
There are several ways of finding the highest common factor of any given set of numbers. This lesson will however focus on only a few of them. These will include;
Note that when working out, any of the methods could be used unless specified.
Example 1
Find the highest common factor of these set of numbers.
Solution
25 = {1, 5, 25}
Common factors = {1, 5}
Highest common factor = {5}
32 = {1, 2, 4, 8, 16, 32}
Common factors = {1, 2, 4, 8}
Highest common factor = {8}
The above examples show the listing method. All the factors of each number are listed. The factors that are common to both numbers are written out and the highest common factor is chosen.
Example 2
Using the ladder method, find the highest common factor of the following sets of numbers
Solution
HCF = 2 X 2 = 4
HCF = 2 X 5 = 10
The method above is known as the ladder method. Numbers are written in columns and only the factors common to both numbers are used. After, the product of the factors is then written out as the prime factor.
Example 3
Another way of finding the HCF of a set of numbers is by the use of the factor tree. The factor tree is a special diagram that displays the factors of a number in the form of a tree.
Find the HCF of these sets of numbers by finding their prime factors using the factor tree.
Solution
Common factor of 15 and 25 = 5
HCF = 5
Common factors = 2 x 2 x 2
HCF = 23
HCF = 8