JSS1: MATHEMATICS - 1ST TERM
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Whole Numbers I | Week 13 Topics|1 Quiz
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Whole Numbers II | Week 21 Topic|1 Quiz
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Counting in Base Two | Week 34 Topics|1 Quiz
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Arithmetic Operations | Week 43 Topics|1 Quiz
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Lowest Common Multiple (LCM) | Week 52 Topics|1 Quiz
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Highest Common Factor | Week 61 Topic|1 Quiz
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Fraction | Week 77 Topics|1 Quiz
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Basic Operations with Fractions I | Week 83 Topics|1 Quiz
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Basic Operations with Fractions II | Week 91 Topic|1 Quiz
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Directed Numbers | Week 103 Topics|1 Quiz
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Estimation and Approximation I | Week 113 Topics|1 Quiz
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Estimation and Approximation II | Week 126 Topics|1 Quiz
Highest Common Factor
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.

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

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