Unit 3 Multiples and factors Unit focus


Learner’s Book page 22


This unit focusses on the following: • prime factors • Lowest Common Multiple (LCM) and Highest Common Factor (HCF) • finding square roots and cube roots using prime factors.


Background information


In order to manage the material on multiples and factors, it is imperative that learners are able to: • do mental calculations with whole numbers including multiplication facts up to 12 × 12


• identify prime numbers up to 100 • determine the LCM and the HCF of numbers to at least 3-digit whole numbers, by inspection or factorisation.


Exercise 1 Guidelines on how to implement this activity


• Revise the prime factorisation of composite numbers within the range of the learner’s knowledge of the multiplication facts (i.e. up to 12 × 12).


• Revise the concepts Highest Common Factor and Lowest Common Multiple by using composite numbers not bigger than 144.


• The Worked examples on page xx are relevant. • Let the learners start Exercise 1 in the class and finish it, if necessary, for homework.


Suggested answers 1


9 = 3 × 3 20 = 2 × 2 × 5 2.1


16 = 2 × 2 × 2 × 2 21 = 3 × 7


42 = 2 × 3 × 7 and 70 = 2 × 5 × 7 HCF ( 42; 70 ) = 2 × 7 = 14


2.2 42 = 2 × 3 × 7 and 70 = 2 × 5 × 7 LCM ( 42; 70 ) = 2 × 3 × 5 × 7 = 210


2.3 132 = 2 × 2 × 3 × 11 and 286 = 2 × 11 × 13 HCF ( 132; 286 ) = 2 × 11 = 22


3.1


4 = 2 × 2, 5 is prime, and 9 = 3 × 3 LCM ( 4; 5; 9 ) = 2 × 2 × 5 × 3 × 3 = 180


3.2 11 is prime, 55 = 5 × 11 and 65 = 5 × 13 LCM ( 11; 55; 65 ) = 5 × 11 × 13 = 715


3.3 48 = 2 × 2 × 2 × 2 × 3, 56 = 2 × 2 × 2 × 7 and 72 = 2 × 2 × 2 × 3 × 3 HCF ( 48; 56; 72 ) = 2 × 2 × 2 = 8


36 Section 4: Teaching Mathematics


18 = 2 × 3 × 3 165 = 3 × 5 × 11


Learner’s Book page 24


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