Types of Numbers

1. Types of Numbers Multiples and LCM Factors and HCF Prime numbers www.mathsrevision.com Prime Decomposition Created by Mr. Lafferty

2. Starter Questions 92o 100o 45o www.mathsrevision.com Created by Mr. Lafferty

3. Types of Numbers Multiples Learning Intention Success Criteria • To be able to write out multiples • We are learning what multiples are . • We are learning how to find the Lowest Common Number. • Use sets of multiples to identify Lowest Common Multiples www.mathsrevision.com Created by Mr. Lafferty

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

5. Types of Numbers Multiples Example : Describe these sets of numbers. 10, 15, 20, 25, 30 “ The multiples of 5 from 10 to 30 “ www.mathsrevision.com Example : Describe these sets of numbers. 54, 60 , 66, 72, 78 “ The multiples of 6 from 54 to 78 “ Created by Mr. Lafferty

6. Types of Numbers Lowest Common Multiple Lowest Common Multiple Smallest Same Number We need to write out multiples in order to find the Lowest Common Multiple. www.mathsrevision.com Created by Mr. Lafferty

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

8. Find the LCM for these numbers CM for 2: 2, 4, 6, 8, 10, 12 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 Mr. Lafferty@mathsrevision.com

9. Lowest Common Multiple Now try TJ3b Ex 1 Ch3 (page 26) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

10. Starter Questions 52o 150o 65o www.mathsrevision.com Created by Mr. Lafferty

11. Types of Numbers Using Factors Learning Intention Success Criteria • To identify factors using factor pairs • We are learning what a factor is. • We are learning to find the Highest Common Factors for a set of numbers. • Find HCF for two numbers by comparing factors. www.mathsrevision.com Created by Mr. Lafferty

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

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

14. Types of Numbers Highest Common Factor Highest Common Factor Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor. www.mathsrevision.com Created by Mr. Lafferty

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

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

17. Highest Common Factor Now try TJ3b Ex 2 Ch3 (page 28) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

18. Starter Questions 4 cm 95o 5 cm www.mathsrevision.com 25o Created by Mr. Lafferty

19. Types of Numbers Prime Numbers Learning Intention Success Criteria • To know the meaning of the term Prime Number. • We are learning what a prime number is and to find all the prime numbers from 1 and 200. • Find all prime numbers between 1 and 200. www.mathsrevision.com Created by Mr. Lafferty

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

21. Strike the two’s, strike the three’s the Sieve of Eratosthenes 25 primes Below 100 when the multiples sublime, the numbers that remain areprime!

22. Use the method of Eratosthenes to find all primes below 200 What is the largest prime <200? 46 primes below 200

23. Range Number of Primes 0 – 1000 168 1000 – 2000 135 2000 – 3000 127 3000 – 4000 120 4000 - 5000 119 5000 - 6000 114 6000 - 7000 117 7000 – 8000 107 8000 - 9000 110 9000 – 10 000 112 ? 10 000 – 11 000 106 11 000 – 12 000 103

24. Strike the two’s, strike the three’s the Sieve of Eratosthenes Worksheet – www.mathsrevision.com when the multiples sublime, the numbers that remain areprime!

25. Strike the two’s, strike the three’s the Sieve of Eratosthenes Worksheet – www.mathsrevision.com when the multiples sublime, the numbers that remain areprime!

26. Highest Common Factor Now try TJ3b Ex 3 Ch3 (page 30) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

27. Starter Questions 119o 5 cm 8 cm www.mathsrevision.com Created by Mr. Lafferty

28. Types of Numbers Prime Decomposition Learning Intention Success Criteria • To know the meaning of the term prime decomposition. • We are learning the technique of prime decomposition . • Decompose numbers to a product of prime only. www.mathsrevision.com Created by Mr. Lafferty

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

30. Types of Numbers 3 6 3 3 2 Prime Decomposition Example : Express 18 as a “product of primes” 18 = 3 x 6 = 3 x 3 x 2 18 All Prime ! www.mathsrevision.com Created by Mr. Lafferty

31. Have you updated your Learning Log ? Highest Common Factor Now try TJ3b Ex 4 Ch3 (page 32) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.