Objectives:
At the end of the lesson, students should be able to:
Example: 1
Write the highest common factor of each of these set of numbers.
Solution
18 = {1, 2, 3, 6, 99, 18}
Common factors {1, 2, 3}
Highest common factor {6}
25 = {1, 5, 25}
Common factors = {1, 5)
Highest common factor = {5}
From the examples above, all the factors of each number are listed.
The factors common to both numbers are then listed or selected. After listing the common factors, the biggest one or the highest factor is chosen.
Example: 2
Find the highest common prime factors of the following set of numbers.
Solution
Common factors of 24 and 32 = 2 x 2 x 2
Highest common factor = 23 = 8
Example: 3
Write the HCF of the following pairs of numbers using the ladder method.
Solution
From the example above, the numbers are divided using a factor that is common to both. The division process is repeated until there are no more common factors. The factors are then listed and multiplied to get the highest common factor.
As in example a, 2 and 5 are common factors. Therefore 2 x 5 = 10 which means that 10 is the highest factor or number that can divide 30 and 40 without a remainder.
Example: 4
Finding the HCF of a set of numbers using a factor tree.
With the aid of a factor tree, find the HCF of these set of numbers.
The common prime factors are 2 x 2 x 3 or 22 x 3
Hence, the HCF of 36 and 60 = 2 x 2 x 3 = 12.