2. Warm Up – write in your notes for todayWrite each number as a product of two whole numbers in as many ways as possible (write the fact families).

1. 62. 163. 174. 36

5. 23

1. Turn in your syllabus and e-mail verification form on the front table if you have not already done so.

3. Objective: Find the prime factorizations of composite numbers. (write in notes)

4. Definitions: prime number, composite number and prime factorization.

5. Grab a whiteboardwhiteboard if you have your own marker and eraser.

6. Work on your MyFace Activity when finished.

1 x 6, 2 x 31 x 16, 2 x 8, 4 x 41 x 171 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6

1 x 23

Welcome to math! Welcome to math! Thursday, July 28Thursday, July 28thth, 2011, 2011

Vocabulary

prime numbercomposite numberprime factorization

Insert Lesson Title Here

A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. Three is a prime number because its only factors are 1 and 3.

A composite number is a whole number that has more than two factors. Six is a composite number because it has more than two factors—1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite.

A composite number can be written as the product of its prime factors. This is called the prime factorization of the number.

You can use a factor tree to find the prime factors of a composite number.

Tell whether each number is prime or composite.

Additional Example 2A & 2B: Identifying Prime and Composite Numbers

A. 23divisible by 1, 23prime

B. 48divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.composite

Additional Example 2C & 2D: Identifying Prime and Composite Numbers

C. 31divisible by 1, 31prime

D. 18divisible by 1, 2, 3, 6, 9, 18composite

Tell whether each number is prime or composite.

Tell whether each number is prime or composite.

Try This: Example 2A & 2B

A. 27divisible by 1, 3, 9, 27composite

B. 24divisible by 1, 2, 3, 4, 6, 8, 12, 24composite

Divisibility RulesDivisibility RulesA number is divisible by. . . Divisible Not Divisible

2 if the last digit is even (0, 2, 4, 6, or 8). 3,978 4,975

3 if the sum of the digits is divisible by 3. 315 139

4 if the last two digits form a number divisible by 4.

8,512 7,518

5 if the last digit is 0 or 5. 14,975 10,978

6 if the number is divisible by both 2 and 3 48 20

9 if the sum of the digits is divisible by 9. 711 93

10 if the last digit is 0. 15,990 10,536

Write the prime factorization of the number.

Example 1: Using a Factor Tree to Find Prime Factorization

A. 2424

8 · 3

4 · 2 · 3

2 · 2 · 2 · 3

Write 24 as the product oftwo factors.

Continue factoring until allfactors are prime.

The prime factorization of 24 is 2 · 2 · 2 · 3. Usingexponents, you can write this as 23 · 3.

Write the prime factorization of the number.

Example B: Using a Factor Tree to Find Prime Factorization

B. 150150

30 · 5

10 · 3 · 5

2 · 5 · 3 · 5

Write 150 as the productof two factors.

Continue factoring until all factors are prime.

The prime factorization of 150 is 2 · 3 · 5 · 5, or2 · 3 · 52.

Try This: Example 1A

Insert Lesson Title Here

Write the prime factorization of the number.

A. 3636

18 · 2

9 · 2 · 2

3 · 3 · 2 · 2

Write 36 as the product oftwo factors.

Continue factoring until allfactors are prime.

The prime factorization of 36 is 2 · 2 · 3 · 3. Usingexponents, you can write this as 22 · 32.

Try This: Example 1B

Insert Lesson Title Here

Write the prime factorization of the number.

B. 9090

45 · 2

9 · 5 · 2

3 · 3 · 5 · 2

Write 90 as the productof two factors.

Continue factoring until all factors are prime.

The prime factorization of 90 is 3 · 3 · 5 · 2, or2 · 32 · 5.

You can also use a step diagram to find the prime factorization of a number…

Steps for Using the Step Diagram for Prime Factorization

1. At each step, divide by the smallest possible prime number.

2. Continue dividing until the quotient is 1.

The prime factors of the number are the prime numbers you divided by.

Write the prime factorization of each number.

Example 3: Using a Step Diagram to Find Prime Factorization

A. 476

476238119

171

22

717

Divide 476 by 2. Write the quotient below 476.

Keep dividing by a prime number.

Stop when the quotient is 1.

The prime factorization of 476 is 2 · 2 · 7 · 17, or22 · 7 · 17.

Write the prime factorization of the number.

Additional Example 2B: Using a Step Diagram to Find Prime Factorization

B. 275

27555111

5511

Divide 275 by 5. Write the quotientbelow 275.

Stop when the quotient is 1.

The prime factorization of 275 is 5 · 5 · 11, or52 · 11.

Try This: Example 4

Insert Lesson Title Here

Write the prime factorization of each number.

A. 324324

16281

27

1

22

33

Divide 324 by 2. Write the quotient below 324.

Keep dividing by a prime number.

Stop when the quotient is 1.

The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or22 · 34.

9333

Try This: Example 2B

Insert Lesson Title Here

Write the prime factorization of the number.

B. 325

32565131

5513

Divide 325 by 5. Write the quotientbelow 325.

Stop when the quotient is 1.

The prime factorization of 325 is 5 · 5 · 13, or52 · 13.

There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result.

476238119

171

22

717

4766834

171

72

217

The prime factorizations are 2 · 2 · 7 · 17 and7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.