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

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

Prime & Composite

Tell whether each number is prime or composite.

23Prime – Only two factors, 1 & 23

129Composite – it has more than two

factors, 1, 3, 43, 129

Practice

Tell whether each number is prime or composite.

19Prime – Only two factors, 1 & 19

21Composite – it has more than two

factors, 1, 3, 7, 21

Practice – You Try!

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

Prime Factorization

Use a factor tree to write the prime factorization of 825.

Factor Tree

825

165

5

33

5

11

3

3(5)2(11)=825

Use a factor tree to write the prime factorization of 150.

Factor Tree – You Try!!

150

305

65

23

2(3)(5)2=150

Use a factor tree to write the prime factorization of 225.

Factor Tree – You Try Again!

225

455

95

33

32(5)2=225

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.

Greatest Common Factor

Find the Greatest Common Factor of 40 and 60

40 60

5 8

42

22

23 x 5 12

5

3 4

2 2

22 x 3 x 5

The GCF of 40 & 60 is: 22 x 5 = 20!!!

22

5

Find the Greatest Common Factor of 6a3b and 4a2b

6 4

2 3

2 x 3 x a3 x b

222 x 2 x a2 x b

The GCF of 6a3b & 4a2b is: 2a2 b!!!

2 a2 b

Find the Greatest Common Factor of 8 and 20

8 20

2 4

22

23

10

2

2 522 x 5

The GCF of 8 & 20 is: 22 = 4!!!

Page 183:

1-14, 17-26, 29-40

Homework!!!