G6 Prime factorization to aid in looking at LCM and HCF.pptx

HCF, LCM, Prime factorization

1. Representing a number as the product of its prime factors F ind the greatest common factor and least common multiple

2. Discuss Quiz Division Q1 Multiplication Q1 Four Operations with negatives and postives - rules

3. 18 September Prime Factorization

4. What is a factor A number that divides another number or expression evenly—i.e., with no remainder . For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

5. List all the factors of: 8 12 30 1, 2, 4, 8 1, 2, 3, 4, 6, 12 1, 2, 3, 5, 6, 10, 15, 30

6. What are prime numbers? Prime numbers are  numbers greater than 1 that only have two factors, 1 and the number itself . This means that a prime number is only divisible by 1 and itself.

7. Why is 1 not a prime number? 1 is not a prime number because it has only one factor, namely 1. Prime numbers need to have exactly two factors.

8. List prime numbers from 1 to 50 The prime numbers from 1 to 50 are:  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

9. Prime factorization of 36 Using repeated Division and Factor Trees

10. List prime numbers from 1 to 50 The prime numbers from 1 to 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

11. Front Tables Jimmy Rudransh Lok Aarushi Angela Shawn Jonathan Ealina Mimi Mohit Back Tables 6A Hiya Daniel Jocelyn Henna Charles Chloe Wendy Cherry Han Emily Lucy

12. Homework

13. Front Tables Lucy Daisy Rachit Mayank Daniel Kayra Devansh Aaron Wendy Lilian Reyansh Back Tables 6B Joyce Donnie Asher Joey Shelby David Curtis Zachary Oly

14. Finding the LCM and the HCF

15. Starter Why is George so upset? What would happen if he buys only one package of hot dogs and one package of hot dog buns? Let’s investigate how many packages of hot dogs and how many packages of hot dog buns he could buy? Knowing what you know about George Banks, how many packages of hot dogs and how many packages of hot dog buns should he buy?

16. In the movie clip there are 8 hot dogs and 12 hot dog buns in a package.

17. What did you find the LCM to be?

18. Lowest Common Multiple (LCM) List as a product of primes Multiply all the prime factors with the highest index Example: LCM of 20 and 12: =60  

19. Highest Common Factor (HCF) List as a product of primes Multiply all the common prime factors with the lowest index Example: HCF of 20 and 12:  

20. Homework

21. Front Tables Lucy Daisy Rachit Mayank Daniel Kayra Devansh Aaron Wendy Lilian Reyansh Back Tables 6B Joyce Donnie Asher Joey Shelby David Curtis Zachary Oly

22. 23 September Finding LCM and HCF

23. How many people were at the dance? When they all danced as couples there was one person left over. When they all danced in threes one person was left over. When they all danced in fours one person was left over. When they all danced in fives one person was left over.

24. LCM of 2, 3, 4, 5 plus 1 LCM = 3x2x2x5=60 60+1 = 61

25.  Two wires are 12 m and 16 m long. The wires are to be cut into pieces of equal length. Find the maximum length of each piece.

26. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 1 × 12, 2 × 6, 3 × 4 1 × 16, 2 × 8, 4 × 4 To find the maximum length, we find the H.C.F. of 12 and 16 12=2x2x3 16=2x2x2x2 HCF=2x2=4 H.C.F. = 4  The maximum length of each piece is 4 m. 

27. Mr B. was celebrating his birthday. He noticed that his age was divisible by 9 and 24. How old was Mr B.?

28. 9=3x3 24= 2x2x2x3 LCM=3x3x2x2x2 = 72 Mr B. Is 72

29. Front Tables Jimmy Rudransh Lok Aarushi Angela Shawn Jonathan Ealina Mimi Mohit Back Tables 6A Hiya Daniel Jocelyn Henna Charles Chloe Wendy Cherry Han Emily Lucy