2. REMEMBER: What is a factor? What are the factors of 24?

3. Common Factors: 1, 2, 4 and 8 What is the Greatest Common Factor (GCF)? First, what is a Common Factor? It is a number that is a factor of two or more numbers. Example: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 4, 5, 8, 10, 20, 40 Factors of 40

4. Find the common factors of: a)3 and 12 b)6 and 18 c)10 and 20 d)24 and 40 e)8 and 20 Common Factors :

5. So, What is the Greatest Common Factor (GCF)? The greatest common factor is the BIGGEST FACTOR that is common to two or more numbers Find the GCF of 40 and 24 24: 40: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 4, 5, 8, 10, 20, 40 What’s the biggest common factor? 8 Example:

6. How can you find the GCF? There are different methods, let’s check two of them.

7. Method 1: Listing the factors a) Find all the Factors of each number, b) Circle the Common factors, c) Choose the Greatest of those Factors of 12 are 1, 2, 3, 4, 6 and 12 Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 GCF: 6 Example 1 : Factors of 12 and 30

8. Example 2: TThe factors of 24 are 11, 2, 3, 4, 6, 8, 12, 24 TThe factors of 36 are 11, 2, 3, 4, 6, 9, 12, 18, 36 TThe common factors of 24 and 36 are 11, 2, 3, 4, 6, 12 TThe Greatest Common Factor of 24 and 36 is 12 GCF(24, 36) = 12

9. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36 The common factors are 1, 2, 3, 4, 6, and 12. ANSWER EXAMPLE 3 The greatest common factor of 48, 24, and 36 is 12. 1, 2, 3, 4, 6, 12 The GCF is 12.

10. Now, Practice: List the factors. Then, find the GCF.

11. We can find the GCF of two or more numbers by listing out the factors of each and identifying the largest common factor But, this could be difficult when the numbers are very large.

12. Method 2: Prime Factorization Another way to find the greatest common factor of two or more numbers is to use the prime factorization of each number. "Prime Factorization" is finding which prime numbers multiply together to make the original number. The product of the common prime factors is the greatest common factor (GCF).

13. Using prime factorization (factor trees) Example 1: Find the GCF of 36 and 48 36 48 66 2 3 2 3 86 24 2 32 22 36: 48: 2233 22223 a) Find the common factors are 2,2,and 3 The GCF is 223 12 b) Multiply them. It is best to start working from the smallest prime number,

14. Find the greatest common factor of 180 and 126 using prime factorization. Begin by writing the prime factorization of each number. 180 10  18 2  5  2  9 2  5  2  3  3 126 2  63 2  3  21 2  3  3  7 180 = 2  2  3  3  5 126 = 2  3  3  7 ANSWER The common prime factors of 180 and 126 are 2, 3, and 3. Using Prime Factorization to Find the GCF EXAMPLE 2 So, the greatest common factor is 2x3x 3 = 18.

15. Practice: Find the GCF using prime factorization