Back to Course

JSS1: MATHEMATICS - 1ST TERM

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

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.

Highest Common Factor

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 

Screen Shot 2021 10 12 at 3.11.32 PM

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 

back-to-top
error: