1. copyright©amberpasillas2010

2. Factor - A whole number or variable expression that divides evenly into a given whole number or variable expression. List all the positive factors of the following. 20 40 120 210 45 140 220 410 58 Make a list! Why do you think I always start with one? copyright©amberpasillas2010

3. Making a list can be helpful to keep track of data and to spot any missing data. Making a list can be helpful to keep track of data and to spot any missing data. To find factors of a number make a list starting with the lowest possible factor which is 1. We start with 1 and work our way up. We know we didn’t miss any factors because our list is organized. copyright©amberpasillas2010

4. When two numbers have the same factor it is called a common factor. Can you think of a common factor for 12 and 6? 2, 3 or 6 copyright©amberpasillas2010

5. Largest number that divides evenly into a given set of numbers. GCF - Greatest Common Factor - There are two ways to find the GCF It is useful to know this for reducing fractions. copyright©amberpasillas2010

6. Ex. Common Factors are 1,2,3,6 GCF= 6 Method # 1 List all the factors of both numbers. Then find the greatest common factor. Factors of 12 1 x 12 2 x 6 3 x 4 Factors of 30 1 x 30 2 x 15 3 x 10 5 x 6 copyright©amberpasillas2010

7. Make a List 60 1 230 320 415 512 610 84 1 242 328 421 614 712 GCF = 12 This method is only useful if both numbers are small copyright©amberpasillas2010

8. Method #1 is great, but you have to list all of the factors for both numbers! This can sometimes take a while! That’s why there is Method # 2 copyright©amberpasillas2010

9. Find the prime factorization of the two numbers. Then multiply their common factors. Factors the 2 numbers have in common are: 2 and 3 Multiply the common factors. GCF: 2 x 3 = 6.6. 12 30 2 6 2 3 2 15 3 5 copyright©amberpasillas2010

10. Prime Factorization 60 2 30 2 15 3 5 84 2 42 2 21 3 7 GCF = 12 copyright©amberpasillas2010

11. Prime Factorization copyright©amberpasillas2010 20 24 2 10 2 5 2 12 2 6 2 3

12. Watch and see why it is important to know GCF! The GCF is used to reduce or to simplify fractions. GCF copyright©amberpasillas2010

13. Simplify or Reduce This Fraction 12 18 2 3 ÷ 6 6 = copyright©amberpasillas2010

14. Take Out Your Study Guide!!! copyright©amberpasillas2010

15. GCF, Make a List Method #1 GCF is the largest number that is a factor of 2 numbers. It is useful to know this for reducing fractions. Ex. Common Factors are 1,2,3,6 GCF= 6 Step 1: List all the factors of both numbers. Step 2: Then find the greatest common factor. #7 Factors of 12 1 x 12 2 x 6 3 x 4 Factors of 30 1 x 30 2 x 15 3 x 10 5 x 6 This method is only useful if both numbers are small

16. copyright©amberpasillas2010 Step 1: Find the prime factorization of the 2 numbers. Step 2: Then multiply their common factors. Factors the 2 numbers have in common are: 2 & 3 Multiply the common factors. #8 12 30 2 6 2 3 2 15 3 5