Ronald Hui Tak Sun Secondary School

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Prime Numbers and Prime Factorization

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Ronald Hui Tak Sun Secondary School Mathematics Ronald Hui Tak Sun Secondary School

Mathematics Keep silence in the class No talking when I talk What should be ready in the next lesson? Textbook Erasable Pens/Pencils Notebook & folder Ronald HUI

Factors (p.0.9) Find all factors of 18. 18  1 = 18  1 is a factor 18  4 = 4.5  4 is NOT a factor 18  5 = 3.6  5 is NOT a factor 18  6 = 3  6 is a factor 18  7 = 2…  7 is NOT a factor Ronald HUI

Factors (p.0.9) Find all factors of 18. 18 = 1 x 18 18 = 2 x 9 18 = 3 x 6 18 = 6 x 3 18 = 9 x 2 18 = 18 x 1 Factors of 18: 1, 2, 3, 6, 9, 18 Ronald HUI

Factors (p.0.9) Factors of 18: 1, 2, 3, 6, 9, 18 Any number is divisible by 1 1 is a factor of any number Even numbers are divisible by 2 2 is a factor of any even number Any number is divisible by itself Any number is a factor of itself Ronald HUI

Prime Numbers (p.0.9) Prime number (質數) Prime number: A natural number (other than 1) which is NOT divisible by any number except 1 and itself Prime number: 2, 3, 5, 7, 11, 13, 17, 19, 23, … Composite number (合成數) 4, 6, 8, 9, 10, 12, 14, 15, 16, … 1 is not prime nor composite Ronald HUI

Prime Factors (p.0.9) Prime factors (質因子) A factor which is prime Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3 All numbers can be expressed as a product of prime factors only – How? Ronald HUI

Index Notation (p.0.10) Factors of 18: 1, 2, 3, 6, 9, 18 18 = 2 x 9 Prime factors of 18: 2, 3 18 = 2 x 9 = 2 x 3 x 3 18 = 2 x 32  Index Notation 32 = 3 x 3 (指數記數法) 3 is base 底 2 is index 指數 Ronald HUI

Index Notation (p.0.10) 32 = 3 x 3 33 = 3 x 3 x 3 34 = 3 x 3 x 3 x 3 3 to the power 2, 3 squared (平方) 33 = 3 x 3 x 3 3 to the power 3, 3 cubed (立方) 34 = 3 x 3 x 3 x 3 35 = 3 x 3 x 3 x 3 x 3 What is 31 ? 31 = 3 Ronald HUI

Index Notation (p.0.10) Index notation is very helpful in long expression of prime factors 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 24 x 33 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 = 27 x 33 x 52 Ronald HUI

Time for Practice Standard Homework 0-B1 PowerPoint files Page 1 http://personal.tsss.edu.hk/roh Ronald HUI

Enjoy the world of Mathematics! Good Luck! Enjoy the world of Mathematics! Ronald HUI