__Objectives:__

At the end of this lesson, students should be able to;

- Write down the common factor of a set of given numbers.
- Write the highest common factor of a set of given numbers by the use of prime factors or factor tree.

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;

- Listing method
- Ladder method
- The factor tree method.

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.

- 15 ad 25
- 24 and 32

__Solution__

- 15 = {1, 3, 5, 15}

25 = {1, 5, 25}

Common factors = {1, 5}

Highest common factor = {5}

- 24 = {1, 2, 3, 4, 6, 8, 12, 24}

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

- 28 ad 36
- 30 and 40

__Solution__

- 28 and 36

HCF = 2 X 2 = 4

- 30 and 40

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.

- 15 and 35
- 24 and 32

__Solution__

- 15 and 25

Common factor of 15 and 25 = 5

HCF = 5

- 24 and 32

Common factors = 2 x 2 x 2

HCF = 2^{3}

^{HCF = 8}

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