2. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers Multiples and LCM Factors and HCF www.mathsrevision.com Prime numbers Prime Decomposition

3. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Starter Questions www.mathsrevision.com 45 o 100 o 92 o

4. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Learning Intention Success Criteria 1.To be able to write out multiples 1.We are learning what multiples are. 2.We are learning how to find the Lowest Common Number. 2.Use sets of multiples to identify Lowest Common Multiples www.mathsrevision.com Types of Numbers Multiples

5. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Multiples Example :Find the first seven multiples of 3. M3 = 3, 6, 9, 12, 15, 18,21 M4 = 4, 8, 12, 16, 20, ……… Example :Find the first five multiples of 4.

6. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Multiples Example :Describe these sets of numbers. 10, 15, 20, 25, 30 54, 60, 66, 72, 78 Example :Find the first five multiples of 4. “ The multiples of 5 from 10 to 30 “ “ The multiples of 6 from 54 to 78 “

7. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Lowest Common Multiple We need to write out multiples in order to find the Lowest Common Multiple. Lowest Common Multiple Smallest Same Number

8. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Lowest Common Multiple Example :Find the LCM of 3 and 4. M3 = 3, 6, 9, 12, 15, ……… M4 = 4, 8, 12, 16, 20, ……… LCM = 12

9. 12-Jan-16Mr. Lafferty@mathsrevision.com CM for 2: 2, 4, 6, 8, 10, 12 Find the LCM for these numbers CM for 5: 5, 10, 15 LCM = 10 CM for 4: 4, 8, 12, 16, 20,24,28,32, 36 CM for 9: 9, 18, 27, 36 LCM =36

10. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Maths Dept. Now try TJ3b Ex 1 Ch3 (page 26) www.mathsrevision.com Lowest Common Multiple

11. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Starter Questions www.mathsrevision.com 65 o 150 o 52 o

12. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Learning Intention Success Criteria 1.To identify factors using factor pairs 1.We are learning what a factor is. 2.We are learning to find the Highest Common Factors for a set of numbers. 2.Find HCF for two numbers by comparing factors. www.mathsrevision.com Types of Numbers Using Factors

13. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Factors Example :Find the factors of 56. F56 =1 and 56 Always divide by 1 and find its pair 2 and 28 4 and 14 7 and 8 From 2 find other factors and their pairs

14. 12-Jan-16Mr. Lafferty@mathsrevision.com F 24 Find the Factors for these numbers 1 24 2 12 3 8 4 6 F 49 1 49 7 7 1, 2, 3, 4, 6, 8, 12, 24 1, 7, 49

15. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Highest Common Factor We need to write out all factor pairs in order to find the Highest Common Factor. Highest Common Factor Largest Same Number

16. MTH 3-05a F12 = 1 and 12 2 and 6 3 4 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Example :Find the HCF of 8 and 12. HCF = 4 F8 =1 and 8 2 4 Highest Common Factor

17. 12-Jan-16Mr. Lafferty@mathsrevision.com F 31 Find the HCF for these numbers 1 31 F 8 1 8 2 4 F 41 1 41 HCF = 1 F 10 1 10 2 5 HCF = 2

18. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Maths Dept. Now try TJ3b Ex 2 Ch3 (page 28) www.mathsrevision.com Highest Common Factor

19. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Starter Questions 5 cm www.mathsrevision.com 4 cm 95 o 25 o

20. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Learning Intention Success Criteria 1.To know the meaning of the term Prime Number. 1.We are learning what a prime number is and to find all the prime numbers from 1 and 200. 2.Find all prime numbers between 1 and 200. www.mathsrevision.com Types of Numbers Prime Numbers

21. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Prime Numbers Definition :A prime number is a number with exactly exactly 2 factors. Example :Is 7 a prime number. Explain? Yes, only two factors 1,7 Example :Is 10 a prime number. Explain? No, more than two factors 1,2,5,10

22. MTH 3-05a Strike the two’s, strike the three’s the Sieve of Eratosthenes when the multiples sublime, the numbers that remain are prime! 25 primes Below 100

23. MTH 3-05a 46 primes below 200 Use the method of Eratosthenes to find all primes below 200 What is the largest prime <  200?

24. MTH 3-05a 10311 000 – 12 000 10610 000 – 11 000 1129000 – 10 000 1108000 - 9000 1077000 – 8000 1176000 - 7000 1145000 - 6000 1194000 - 5000 1203000 – 4000 1272000 – 3000 1351000 – 2000 1680 – 1000 Number of PrimesRange ?

25. MTH 3-05a Strike the two’s, strike the three’s the Sieve of Eratosthenes when the multiples sublime, the numbers that remain are prime! Worksheet – www.mathsrevision.com

26. MTH 3-05a Strike the two’s, strike the three’s the Sieve of Eratosthenes when the multiples sublime, the numbers that remain are prime! Worksheet – www.mathsrevision.com

27. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Maths Dept. Now try TJ3b Ex 3 Ch3 (page 30) www.mathsrevision.com Highest Common Factor

28. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Starter Questions 8 cm www.mathsrevision.com 5 cm 119 o

29. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Learning Intention Success Criteria 1.To know the meaning of the term prime decomposition. 1.We are learning the technique of prime decomposition. 2.Decompose numbers to a product of prime only. www.mathsrevision.com Types of Numbers Prime Decomposition

30. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com A number is either Prime or Composite. (except for 0) If it is composite, like 12, it can always be expressed as a “product of primes” Example :Express 12 as a “product of primes” Prime Decomposition 12 3 34 22 12 = 3 x 4 = 3 x 2 x 2 All Prime !

31. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Example :Express 18 as a “product of primes” Prime Decomposition 18 3 36 23 18 = 3 x 6 = 3 x 3 x 2 All Prime !

32. MTH 3-05a 12-Jan-16Created by Mr. Lafferty Maths Dept. Now try TJ3b Ex 4 Ch3 (page 32) www.mathsrevision.com Highest Common Factor Have you updated your Learning Log ?