Back to Course

JSS1: MATHEMATICS - 1ST TERM

0% Complete
0/0 Steps
  1. Whole Numbers I | Week 1
    3 Topics
    |
    1 Quiz
  2. Whole Numbers II | Week 2
    1 Topic
    |
    1 Quiz
  3. Counting in Base Two | Week 3
    4 Topics
    |
    1 Quiz
  4. Arithmetic Operations | Week 4
    3 Topics
    |
    1 Quiz
  5. Lowest Common Multiple (LCM) | Week 5
    2 Topics
    |
    1 Quiz
  6. Highest Common Factor | Week 6
    1 Topic
    |
    1 Quiz
  7. Fraction | Week 7
    7 Topics
    |
    1 Quiz
  8. Basic Operations with Fractions I | Week 8
    3 Topics
    |
    1 Quiz
  9. Basic Operations with Fractions II | Week 9
    1 Topic
    |
    1 Quiz
  10. Directed Numbers | Week 10
    3 Topics
    |
    1 Quiz
  11. Estimation and Approximation I | Week 11
    3 Topics
    |
    1 Quiz
  12. Estimation and Approximation II | Week 12
    6 Topics
    |
    1 Quiz
  • excellence
  • Follow

Lesson Progress
0% Complete

Topic Content:

  • Meaning of Highest Common Factor (HCF)
  • Worked Examples

What is the Highest Common Factor?

The Highest Common Factor (HCF) is 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 the Highest Common Factor. 

There are two methods of solving HCF just like LCM 

1. Listing method 
2. Product of their prime 

Worked Example 6.1.1:

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 Factors, we can easily find the HCF as follows: 

a. Express the numbers as a product of the prime factors.
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.

Screenshot 2023 08 19 at 02.03.26

24 = 2 × 2 × 2 × 3 
30 = 2 × 3 × 5 

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

⇒ HCF = 2 × 3 = 6 

Worked Example 6.1.2:

Find the HCF of 18, 24, and 42. 

18 = 2 × 3 × 3 
24 = 2 × 2 × 2 × 3 
42 = 2 × 3 × 7 

The common prime factors are 2 and 3 

The HCF = 2 × 3 = 6 

Worked Example 6.1.3:

Find the HCF of 216, 288, 360 

Screenshot 2023 08 19 at 02.11.58

216 = 2 × 2 × 2 × 3 × 3 × 3
288 = 2 × 2 × 2 × 2 × 2 × 3 × 3
360 = 2 × 2 × 2 × 3 × 3 × 5

The prime factors in index notation 

216 = 23 × 33
288 = 25 × 32
360 = 23 × 32 × 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 × 32) × 3 
288 = (23 × 32) × 22
360 = (23 × 32) × 5 

The HCF = 23 × 32 = 8 × 9 = 72