JSS2: MATHEMATICS  1ST TERM

Properties of Whole Numbers I  Week 14 Topics1 Quiz

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Properties of Whole Numbers III  Week 35 Topics1 Quiz

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Laws of Indices  Week 55 Topics1 Quiz

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Fractions, Ratios, Proportions & Percentages I  Week 96 Topics1 Quiz

Fractions, Ratios, Proportions & Percentages II  Week 104 Topics1 Quiz

Fractions, Ratios, Proportions & Percentages III  Week 113 Topics1 Quiz

Approximation & Estimation  Week 121 Topic1 Quiz
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Highest Common Factors (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 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 ofÂ
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.
2^{2 }x 3^{3} x 5
2^{3} x 3^{2} x 5^{2} x 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.
Hence, the common factors are 2, and 2.
HCF of 12 and 16 = 2 Ã— 2 = 4
Method 2: Prime Factorization Method
Express each number as a product of its prime factors and multiply their common prime factors.
HCF = 2 x 2 = 4
b. 18, 27 and 36
Method 1
HCF = 3 x 3 = 9
Method 2
18 = 2 Â xÂ Â 3 Â x Â 3
27 = 3 Â xÂ Â 3 Â Â xÂ Â 3
36 = 2 Â x Â 2 Â xÂ 3Â x Â 3
HCF = 3 x 3 = 9
c.
2 x 2 x 3 x 5 x 7 Â Â Â Â
2 x 2 x 2 x 2 x 7
HCF = 2 x 2
= 4
d.
2^{2} x 3^{3} x 5
2^{3}Â xÂ 3^{2}Â xÂ 5^{2}Â 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.
HCF = 2^{2} x 3^{2} x 5
= 4 x 9 x 5 = 180
Â Note:
2^{2}Â and 2^{3} The indexÂ (power) â€˜2â€™ isÂ lower than 3
3^{3} and 3^{2} The index â€˜2â€™ is lower than 3
5^{1} and 5^{2} The index â€˜1â€™ is lower than 2
2^{2} Â is less than (<) Â 2^{3}Â
3^{2}Â is less than (<)Â 3^{3}Â
5^{1} Â is less than (<)Â 5^{2}
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