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copyright©amberpasillas2010 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 Why do you 1 20 1 40 think I always 2 20 Make 2 10 start with one? 4 5 4 10 a list! 5 8 copyright©amberpasillas2010 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 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 GCF- Greatest Common Factor - Largest number that divides evenly into a given set of numbers. It is useful to know this for reducing fractions. There are two ways to find the GCF copyright©amberpasillas2010 Method # 1 List all the factors of both numbers. Then find the greatest common factor. Ex. Factors of 12 1 x 12 2x 6 3x 4 Factors of 30 1 x 30 2 x 15 3 x 10 5x 6 Common Factors are 1,2,3,6 GCF= 6 copyright©amberpasillas2010 Make a List 60 1 60 2 30 3 20 4 15 5 12 6 10 84 1 84 2 42 3 28 4 21 6 14 7 12 GCF = 12 copyright©amberpasillas2010 This method is only useful if both numbers are small 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 Find the prime factorization of the two numbers. Then multiply their common factors. 30 12 2 2 15 6 2 3 3 2 23 5 2 3 5 Factors the 2 numbers have in common are: 2 and 3 Multiply the common factors. GCF: 2 x 3 = 6. copyright©amberpasillas2010 Prime Factorization 60 84 2 2 30 15 2 3 42 21 2 5 3 7 2 2 3 5 2 2 3 7 GCF 2 2 3 GCF = 12 copyright©amberpasillas2010 Prime Factorization 24 20 2 10 2 2 12 5 2 25 6 2 2 3 2 2 23 GCF 2 2 4 copyright©amberpasillas2010 Watch and see why it is important to know GCF! The GCF is used to reduce or to simplify fractions. 32 2 16 2 8 2 4 2 2 48 2 24 2 12 2 6 2 3 32 16 2 48 16 3 GCF copyright©amberpasillas2010 Simplify or Reduce This Fraction 12 6 2 ÷ = 18 6 3 copyright©amberpasillas2010 Take Out Your Study Guide!!! copyright©amberpasillas2010 #7 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. Step 1: List all the factors of both numbers. Step 2: Then find the greatest common factor. Ex. Factors of 12 1 x 12 2x 6 3x 4 Factors of 30 1 x 30 2 x 15 3 x 10 5x 6 Common Factors are 1,2,3,6 GCF= 6 This method is only useful if both numbers are small copyright©amberpasillas2010 #8 Find the prime factorization of the 2 numbers. Step 2: Then multiply their common factors. Step 1: 30 12 2 2 15 6 2 3 3 2 23 5 2 3 5 Factors the 2 numbers have in common are: 2 & 3 Multiply the common factors. GCF 2 3 6 copyright©amberpasillas2010