To Start: 10 Points!!! Simplify and Evaluate: (-4)5 =(-4)(-4)(-4)(-4)(-4) = -4,096!! 2x3 + 4y, for x=-3 and y=2 2(-3)3 + 4(2) 2(-27) + 8 -54 + 8 -46!!!!

Chapter 4: Factors, Fractions, and Exponents Section 4.3: Prime Factorization and Greatest Common Factor

Prime & Composite A prime number is a positive integer greater than 1 with exactly two factors, one and the number itself. Ex. 2, 3, 5, 7 A composite number is a positive integer greater than 1 with more than two factors. Ex. 4, 6, 8, 9, 10

Practice Tell whether each number is prime or composite. 23 Prime – Only two factors, 1 & 23 129 Composite – it has more than two factors, 1, 3, 43, 129

Practice – You Try! Tell whether each number is prime or composite. 19 Prime – Only two factors, 1 & 19 21 Composite – it has more than two factors, 1, 3, 7, 21

Prime Factorization Writing a composite number as a product of its prime factors shows the prime factorization of the number. We will use a factor tree to find prime factorizations

Factor Tree Use a factor tree to write the prime factorization of 825. 825 5 165 5 33 3(5)2(11)=825 3 11

Factor Tree – You Try!! 2(3)(5)2=150 Use a factor tree to write the prime factorization of 150. 150 5 30 5 6 2(3)(5)2=150 3 2

Factor Tree – You Try Again! Use a factor tree to write the prime factorization of 225. 225 5 45 5 9 32(5)2=225 3 3

Greatest Common Factor Any factors that are the same for two or more numbers are common factors. The greatest of these common factors is called the Greatest Common Factor. We will use prime factorization to find the GCF. If there are no prime factors in common, then the GCF is 1.

Find the Greatest Common Factor of 40 and 60 23 x 5 5 12 5 8 22 x 3 x 5 2 4 3 4 22 5 2 2 2 2 The GCF of 40 & 60 is: 22 x 5 = 20!!!

Find the Greatest Common Factor of 6a3b and 4a2b 2 x 3 x a3 x b 2 x 2 x a2 x b 2 3 2 2 2 a2 b The GCF of 6a3b & 4a2b is: 2a2 b!!!

Find the Greatest Common Factor of 8 and 20 23 2 10 2 4 22 x 5 2 2 2 5 The GCF of 8 & 20 is: 22 = 4!!!

Homework!!! Page 183: 1-14, 17-26, 29-40