1. CONFIDENTIAL 1 GREATEST COMMON FACTOR

2. CONFIDENTIAL 2 LET’S CHECK WHAT WE KNOW 1. Tell whether each number is divisible by 2, 3, 4, 5, 6, 9 or 10. 1. 67 2. 145 3. 891 4. 202 2. Find the Prime factorization of: i) 63 ii) 8 iii) 120 iv) 264 v) 28

3. CONFIDENTIAL 3 FACTORS When a number divides another number exactly, the first number is called the factor of the second. 1 is a factor of every number. The greatest factor of the number is the number itself. If a number can divide another number leaving no remainder, it is a factor. FACTOR FACTS

4. CONFIDENTIAL 4 FINDING FACTORS Find the factors of 24 Since 1 is a factor of every number, it is a factor of 24. 24 ÷ 2 = 12; 24 ÷ 3 = 8; 24 ÷ 4 = 6; 24 ÷ 6 =4; 24 ÷8 = 3; 24 ÷ 12 = 2. Also, 24 is the factor of itself. Therefore, the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 Finding factors is easy

5. CONFIDENTIAL 5 Do some problems to find factors Find the factors of the following numbers: 1.36 2.42 3.35 4.33 5.21 Let’s do it !

6. CONFIDENTIAL 6 Use of a Venn Diagram to represent common factors A Venn Diagram uses overlapping circles to show the similarities and differences of two groups of items. Any item that is located where the circles overlap has a characteristic of both circles.

7. CONFIDENTIAL 7 Representation of Factors and Common factors in a Venn Diagram The Venn Diagram below shows the common factors of 12 and 18 Factors of 12 Factors of 18 4 12 9 18 1, 2 3, 4 The common factors are 1, 2, 3, 4.

8. CONFIDENTIAL 8 Finding Common Factors Find the common factors using Venn Diagram: 1.9 and 15 2.18 and 24 3.15 and 35

9. CONFIDENTIAL 9 Greatest Common Factor (GCF) Numbers often have common factors. The greatest of the common factors of two or more numbers is the Greatest Common Factor (GCF) of the numbers.

10. CONFIDENTIAL 10 Have a break !!!

11. CONFIDENTIAL 11 How to find the greatest common factor Find the GCF of 8 and 12 Factors of 8Factors of 12 8 1 2 4 3 6 12 The common factors are 1, 2, 4. The greatest common factor among them is 4

12. CONFIDENTIAL 12 Try to do it Find the GCF with the help of Venn Diagram a. 48 and 96 b. 35 and 60 c. 12 and 13

13. CONFIDENTIAL 13 Finding the GCF by Listing Factors Find the GCF of 20 and 30 Factors of 20 1, 20 2, 10 4, 5 Factors of 30 1, 30 2, 15 3, 10 5, 6 The common factors are 1, 2, 5 and 10. The greatest among them is 10. GCF = 10

14. CONFIDENTIAL 14 Now your turn Find the GCF of the following by listing the factors: 1. 25 and 28 2. 15 and 30 3. 24 and 48

15. CONFIDENTIAL 15 Find the GCF by using Prime Factors Find the GCF of 20 and 35 Method 1 20 2 10 252 35 57 The common factor is 5 and GCF is 5 20, 35 4, 7 5 Method 2 Divide 20 and 35 by 5 Since we will not be able to divide 4 and 7 with the same number, 5 is the GCF

16. CONFIDENTIAL 16 Let’s look at another example! 36 and 24 share two 2’s and one 3 in common. GCF: 12 36: 2, 2, 3, 324: 2, 2, 2, 3

17. CONFIDENTIAL 17 The GCF of two or more numbers is the product of the common prime factors of the numbers. Example: Find the GCF of 18 and 24 GCF of two or more numbers 2 18, 24 3 9, 12 3, 4 The quotients cannot be divided further by a common prime factor GCF = 2X3 = 6

18. CONFIDENTIAL 18 Now try to do it Find the GCF by prime factorization method: i)36, 48 ii)72, 81 iii)99,110

19. CONFIDENTIAL 19 What is hidden? http://www.thekidzpage.com/onlinejigsawpu zzles/kids-jigsaw-puzzles/12-piece-jigsaw/08- 08-06-spider.htmlwww.thekidzpage.com/onlinejigsawpu zzles/kids-jigsaw-puzzles/12-piece-jigsaw/08- 08-06-spider.html

20. CONFIDENTIAL 20 Practice Problems I. Find the GCF with the help of Venn Diagrams a) 10, 30 b) 12,18 II. Find the GCF by listing factors: a) 18, 42 b) 16, 52, 76 III. Find the GCF by prime factorization: a) 36, 90 b) 9, 18, 42 Wow!!!

21. CONFIDENTIAL 21 Use GCF to solve real life situations Mr. Stephan has 4 storage cases that can hold 16, 24,36 and 48 files. The cases have sections holding the same number of files. What is the greatest number of files in a section? 216, 24, 36 2 8, 12, 18 4, 6, 9 The quotients cannot be divided further by a common prime factor The greatest number of files in a section is 4

22. CONFIDENTIAL 22 Solve this problem with GCF Mohammed wants to put 45 rose plants, 81 orchids and 63 hibiscus plants in his garden. If he puts the same number of plants in each row and each row has only type of plant. What is the greatest number of plants he can put in one row? How to do this? Hmmm…..

23. CONFIDENTIAL 23 Assignment 1) 9, 18 and 42 Find the GCF using Venn Diagram Find the GCF by Listing Factors 2) 12, 36, 48 Find the GCF by Prime Factorization 3) 27, 54, 18 I can do it…

24. CONFIDENTIAL 24 Review Greatest Common FactorGreatest Common Factor The greatest of the common factors of two or more numbers is the Greatest Common Factor (GCF) of the numbers. There are two ways to find GCF: −Make a list of factors −Use Prime Factorization

25. CONFIDENTIAL 25 Great Job!