1. 11/29/11 Turn in any make up work you completed over the break! Bellringer: Write down one thing about your break. Turn in any make up work you completed over the break! Bellringer: Write down one thing about your break.

2. Finding The Greatest Common Factor

3. Greatest Common Factor The greatest common factor is the largest common factor of two numbers. Factors are all of the numbers that divide into a given number equally. The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers The greatest common factor is the largest common factor of two numbers. Factors are all of the numbers that divide into a given number equally. The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers

4. Finding Factors Find the factors of 18 1 goes into 18, 18 times. 2 goes into 18, 9 times. 3 goes into 18, 6times. 4 does not divide 18 evenly. 5 does not divide 18 evenly. We are now back to 6. We have found all factors of 18. 1, 2, 3, 6, 9, and 18 Find the factors of 18 1 goes into 18, 18 times. 2 goes into 18, 9 times. 3 goes into 18, 6times. 4 does not divide 18 evenly. 5 does not divide 18 evenly. We are now back to 6. We have found all factors of 18. 1, 2, 3, 6, 9, and 18

5. Finding The GCF Using Factors Determine the greatest common factor of two numbers by finding all the factors for the two numbers then comparing them. The largest common factor of the two numbers is their greatest common factor.

6. Think Backwards… Find Factors Circle Common Factors Group Greatest Factor Find Factors Circle Common Factors Group Greatest Factor

7. Step 1: Find the Factors 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

8. Step 2: Circle Common Factors 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

9. Step 3: Group the Greatest Factor 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

10. The Greatest Common Factor of 24 and 36 is… 12

11. Find the GCF of 12 and 24 Step 1: Find the factors 12 – 24 – Step 1: Find the factors 12 – 24 –

12. Find the GCF of 12 and 24 Step 2: Circle the common factors 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24 Step 2: Circle the common factors 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24

13. Find the GCF of 12 and 24 Step 3: Group the greatest factor 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24 Step 3: Group the greatest factor 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24

14. The Greatest Common Factor of 12 and 24 is … 12

15. Using Factors Again Find the GCF of 15 and 100 Factors of 15: Factors of 100: The greatest common factor of 15 and 100 is Find the GCF of 15 and 100 Factors of 15: Factors of 100: The greatest common factor of 15 and 100 is

16. Your turn! Find the Greatest Common Factor of 16 and 20. Remember…Find Factors, Circle Common, Group Greatest! Find the Greatest Common Factor of 16 and 20. Remember…Find Factors, Circle Common, Group Greatest!

17. The Greatest Common Factor of 16 and 20 is… 44

18. Exit Ticket What is the GCF of 15 and 30?

19. 11/30 Get out your homework. Bellringer: Multiply WITHOUT A CALCULATOR! 5x6 -4x3 -7x-6 Get out your homework. Bellringer: Multiply WITHOUT A CALCULATOR! 5x6 -4x3 -7x-6

20. Homework answers 1.4 2.5 3.8 4.1 5.4 1.4 2.5 3.8 4.1 5.4

21. Finding the Prime Factorization A prime factorization is when a product is broken down until only prime numbers remain. Prime numbers are numbers who’s only factors are 1 and them self. A factor tree is useful in finding a prime factorization.

22. Prime Factorization Break 18 down to only prime numbers. 18 /\ 29 /\ 3 3 18 = 2 × 3 × 3 Break 18 down to only prime numbers. 18 /\ 29 /\ 3 3 18 = 2 × 3 × 3

23. Finding the GCF Using Prime Factorization To determine the greatest common factor, find the prime factorization for each number. Find all of the common prime factors of the two numbers and multiply them together. Your sum is the GCF.

24. Using Prime Factorization Find the GCF of 36 and 24 36 24 /\ /\ Find the GCF of 36 and 24 36 24 /\ /\

25. Using Prime Factorization Again Find the GCF of 21 and 42 21 42 Find the GCF of 21 and 42 21 42

26. GCF worksheet Complete questions 6-10.