Lesson 6, Topic 1
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# Highest Common Factor

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Highest Common Factor (HCF): the biggest number that will divide two or more numbers.

2, 7, and 14 are common factors of 28, 42, and 70:

14 is the greatest of the three common factors.

We say that 14 is the highest common factor of 28, 42, and 70.

HCF is short for Highest Common Factor.

There are two methods of solving HCF just like LCM

1. Listing method

2. Product of their prime

Example 1

Find the HCF of 24 and 30

Solution

Using the first method: Listing Method

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Factors of 30 = 1, 2, 3, 5, 6 , 10, 15, 30

The highest factor common to both numbers is 6. Therefore, the HCF of 30 and 24 is 6.

Using the second method: Product of their prime. We can easily find the HCF as follows:

a. Express the numbers as a product of prime factor

b. Select the prime factors that are common to all the numbers

c. Find the product of these prime factors i.e. multiply them together.

30 = 2 x 3 x 5

24 = 2 x 2 x 2 x 3

Note: the prime factors that are common to both numbers are 2 and 3

:- HCF = 2 x 3 = 6

Example 2

Find the HCF of 18, 24, 42.

18 = 2 x 3 x 3

24 = 2 x 2 x 2 x 3

42 = 2 x 3 x 7

The common prime factors are 2 and 3

The HCF = 2 x 3 = 6

Example 3

Find the HCF of 216, 288, 360

216 = 2 x 2 x 2 x 3 x 3

288 = 2 x 2 x 2 x 2 x 2 x 3 x 3

360 = 2 x 2 x 2 x 3 x 3 x 5

The prime factors in index notation

216 = 23 x 33

288 = 25 x  32

360 = 23 x 32 x 5

23 is the lowest power of 2 contained in the three numbers. Thus the HCF contains 23

32 is the lowest power of 3 contained in the three numbers. The HCF contains 32

216 = (23 x 33) x 3

288 = (23 x 32) x 22

360 = (23 x 32) x 5

The HCF = 23 x 32 = 8 x 9 = 72 error: