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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4Topics
    |
    2 Quizzes
  2. Properties of Whole Numbers II | Week 2
    4Topics
    |
    2 Quizzes
  3. Properties of Whole Numbers III | Week 3
    4Topics
    |
    1 Quiz
  4. Indices | Week 4
    2Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1Topic
    |
    1 Quiz
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The highest common factors (HCF) of two or more numbers is the greatest of the factors common to them.

There are different methods of finding H.C.F. of two or more numbers. 2 of those methods are;

1. Short division method

2. Prime Factorization Method

Example 1

Find the HCF of 

a. 12 and 16

b. 18 , 27 and 36

c.

2 x 2 x 3 x 5 x 7

2 x 2 x 2 x 2 x 7

d.

22 x 33 x 5

23 x 32 x 52

Solution

a. 12 and 16

Method 1: divide each number by common prime factors (Short Division Method)

  • 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.
HCF

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.

Screen Shot 2020 11 21 at 7.55.17 PM
Screen Shot 2020 11 21 at 7.57.18 PM

HCF  =  2 x 2 = 4

b. 18, 27 and 36

Method 1

hcf jss2

HCF =  3 x 3 = 9

Method 2

Screen Shot 2020 11 21 at 8.08.32 PM

18 = 2   x    3   x   3

27 = 3   x    3     x    3

36 = 2   x   2   x  3  x   3

hcf e1605986550130

HCF  = 3 x 3 = 9

c.

2 x 2 x 3 x 5 x 7        

2 x 2 x 2 x 2 x 7

Screen Shot 2021 09 19 at 12.20.22 AM

HCF   =   2 x  2

=   4

d.

22 x 33 x 5

23  x  32  x  52  x 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   x  32   x  5

=   4  x 9 x 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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