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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4 Topics
    |
    1 Quiz
  2. Properties of Whole Numbers II | Week 2
    4 Topics
    |
    1 Quiz
  3. Properties of Whole Numbers III | Week 3
    5 Topics
    |
    1 Quiz
  4. Indices | Week 4
    2 Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5 Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4 Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3 Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4 Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6 Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4 Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3 Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1 Topic
    |
    1 Quiz



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Topic Content:

  • Meaning of Highest Common Factor (HCF)
  • Different Methods of Finding HCF

What is HCF?

The highest common factor (HCF) of two or more numbers is the greatest of the factors common to them.

There are different methods of finding HCF of two or more numbers. 2 of those methods are;

1. Short division method
2. Prime Factorization Method

Worked Example 1.3.1:

Find the HCF of 

a. 12 and 16

b. 18, 27 and 36

c.
2 × 2 × 3 × 5 × 7
2 × 2 × 2 × 2 × 7

d.
22 × 33 × 5
23 × 32 × 52 × 7

Solution

a. 12 and 16

Method 1: (Short Division Method)

Applying this method, we divide each number by common prime factors. The steps are as follows:

  • Write the numbers in individual rows.
  • Divide the numbers by common prime factors.
  • Factorisation stops when we reach prime numbers which cannot be further divided.
  • HCF is the product of all the common factors.
Screenshot 2023 08 19 at 15.12.18

Hence, the common factors are 2, and 2.

HCF of 12 and 16 = 2 × 2 = 4

Method 2: Prime Factorization Method

Express each number as a product of its prime factors and multiply their common prime factors.

Screenshot 2022 12 22 at 14.57.43
Screenshot 2023 08 19 at 15.21.34

HCF  =  2 × 2 = 4

b. 18, 27 and 36

Method 1:

Screenshot 2023 08 19 at 15.25.40

HCF =  3 × 3 = 9

Method 2:

Screenshot 2023 08 19 at 15.32.36

18 = 2   ×    3   ×  3
27 = 3   ×    3   ×  3
36 = 2   ×   2   ×  3  ×   3

hcf e1605986550130

HCF  = 3 × 3 = 9

c.

2 × 2 × 3 × 5 × 7        
2 × 2 × 2 × 2 × 7

Screenshot 2023 08 19 at 15.50.30

HCF   =   2 × 2

=   4

d.

22 × 33 × 5
23  ×  32  ×  52  × 7

In this case, the easiest way is to compare powers of the same base. The one with the lowest power is a common factor.

Screen Shot 2020 11 21 at 8.27.03 PM

HCF  =   22   ×  32   ×  5

=   4 Ã— 9 × 5  =  180

 Note:
22  and 23 The index  (power) ‘2’ is  lower than 3
33 and 32 The index ‘2’ is lower than 3
51 and 52 The index ‘1’ is lower than 2
22   is less than (<)   23 
32  is less than (<)  33 
51   is less than (<)  52

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