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FACTOR TREES Definition Prime Factorization-When you write a number as a product of prime numbers, you are writing its prime factorization. You can use a diagram called a factor tree to write the prime factorization of a number. Example 200 2 100 2 50 2 25 5 5 Factor Tree PRIME & COMPOSITE #’S A prime number is a whole number that is greater than 1 and has EXACTLY two whole number factors, 1 and itself. A composite number is a whole number that is greater than 1 and has more than two whole number factors. The number 1 is neither prime nor composite. EX: (24: 1,2,3,4,6,8,12,24) Composite EX: (41:1,41) Prime FACTOR TREE’S A diagram that can be used to write the prime factorization of a number. 20 2 2 10 5 GCF The GCF(Greatest Common Factor) is the most common factor in the two numbers like 15 and 18 there most common factor is 3. 15 3 18 5 2 3 15:3,5 18:2,9,3,3 Both have a three so that is their GCF. 9 3 LCM The LCM(Least Common Multiple) is the lowest multiple in two numbers like 9 and 5. 9 3 5 3 9:3,3 5:5 It has to be 3x3x5=45, so the LCM is 45 for 9 and 5 Another way to do a Factor Tree is to number them off by their factors. 20:1,2,4,5,20 20’s factors are 1,2,4,5,and 20 FACTORS MONOMIAL A monomial is a number, a variable, or the product of a number and one or more variables raised to whole number powers. EX. 28xy3=2*2*7*x*y3 =2*2*7*x*y*y*y RELATIVELY PRIME Two or more numbers are relatively prime if their greatest common factor is 1. EX: 3 and 5 GCF:1 EXAMPLES 15 3 20 5 2 2 48 10 2 5 2 2 2 15:3,5 20:2,2,5 48:2,2,2,2,3 24 12 6 3