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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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