JSS2 First Term Mathematics Lesson Note – Whole Numbers II

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WEEK 2

WHOLE NUMBERS

CONTENTS

• Revision: Prime factors, LCM and HCF
• Squares and square roots
• Quantitative reasoning.

Prime factors, LCM and HCF

Prime factors of numbers.

Prime factors of a number are the factors of that number which are not divisible by any other number except that number and 1. For example, the prime factors of 30 are 2,3 and 5 because out of all the factors of 30 (1,2,3,5,6,10,15 and 30), it is only 2,3 and 5 that are not divisible by any other number except themselves and 1.

Examples:

Write the factors of the following numbers and state the prime factors, hence express each number as a product of its prime factors.

• 22 (b) 50              (c) 63               (d) 42

Solutions:                      

• 22

Factors of 22 are 1, 2, 11, 22

The prime factors of 22 are 2 and 11

Product of its prime factors of 22 = 2 x11

• Factors of 50 are 1, 2, 5, 10, 25 and 50

The prime factors of 50 are 2 and 5

Product of its prime factors of 50 = 2 x 5 x 5 = 2 x 5²

• Factors of 63 are 1, 3, 7, 9, 21 and 63

The prime factors of 63 are 3 and 7

Product of its prime factors of 63 = 3 x 3 x 7 = 3² x 7

• Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42

The prime factors of 42 are 2, 3 and 7

Product of its prime factors of 42 = 2 x 3 x 7

Prime factorization

Examples

Express the following as a product of their prime factors in index form.

(a) 27   (b) 104   (c) 116

Solutions:                      

Divide each of the numbers by the prime factors in turns until it will not divide any further.

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