1. Welcome to math! Thursday, July 28th, 2011
1. Turn in your syllabus and verification form on the front table if you have not already done so.
2. Warm Up – write in your notes for today
Write each number as a product of two whole numbers in as many ways as possible (write the fact families).
1. 6
2. 16
3. 17
4. 36
5. 23
1 x 6, 2 x 3
1 x 16, 2 x 8, 4 x 4
1 x 17
1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6
1 x 23
3. Objective: Find the prime factorizations of composite numbers. (write in notes)
4. Definitions: prime number, composite number and prime factorization.
5. Grab a whiteboard if you have your own marker and eraser.
6. Work on your MyFace Activity when finished.

2. Insert Lesson Title Here
Vocabulary
prime number
composite number
prime factorization

3. 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.

4. A composite number is a whole number that has more than two factors
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.

5. Additional Example 2A & 2B: Identifying Prime and Composite Numbers
Tell whether each number is prime or composite.
A. 23
divisible by 1, 23
prime
B. 48
divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
composite

6. Additional Example 2C & 2D: Identifying Prime and Composite Numbers
Tell whether each number is prime or composite.
C. 31
divisible by 1, 31
prime
D. 18
divisible by 1, 2, 3, 6, 9, 18
composite

7. Try This: Example 2A & 2B
Tell whether each number is prime or composite.
A. 27
divisible by 1, 3, 9, 27
composite
B. 24
divisible by 1, 2, 3, 4, 6, 8, 12, 24
composite

8. Divisibility Rules A 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

9. Example 1: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of the number.
A. 24
Write 24 as the product of
two factors. 24
8 · 3
Continue factoring until all
factors are prime.
4 · 2 · 3
2 · 2 · 2 · 3
The prime factorization of 24 is 2 · 2 · 2 · 3. Using
exponents, you can write this as 23 · 3.

10. Example B: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of the number.
B. 150
150
Write 150 as the product
of two factors.
30 · 5
Continue factoring until
all factors are prime.
10 · 3 · 5
2 · 5 · 3 · 5
The prime factorization of 150 is 2 · 3 · 5 · 5, or
2 · 3 · 52.

11. Insert Lesson Title Here
Try This: Example 1A
Write the prime factorization of the number.
A. 36
Write 36 as the product of
two factors. 36
18 · 2
Continue factoring until all
factors are prime.
9 · 2 · 2
3 · 3 · 2 · 2
The prime factorization of 36 is 2 · 2 · 3 · 3. Using
exponents, you can write this as 22 · 32.

12. Insert Lesson Title Here
Try This: Example 1B
Write the prime factorization of the number.
B. 90 90
Write 90 as the product
of two factors.
45 · 2
Continue factoring until
all factors are prime.
9 · 5 · 2
3 · 3 · 5 · 2
The prime factorization of 90 is 3 · 3 · 5 · 2, or
2 · 32 · 5.

13. Steps for Using the Step Diagram for Prime Factorization
You can also use a step diagram to find the prime factorization of a number…
Steps for Using the Step Diagram for Prime Factorization
At each step, divide by the smallest possible prime number.
Continue dividing until the quotient is 1.
The prime factors of the number are the prime numbers you divided by.

14. Example 3: Using a Step Diagram to Find Prime Factorization
Write the prime factorization of each number.
A. 476
Divide 476 by 2. Write the
quotient below 476. 2
476 2
238
Keep dividing by a prime
number. 7
119 17 17 1
Stop when the quotient is 1.
The prime factorization of 476 is 2 · 2 · 7 · 17, or
22 · 7 · 17.

15. Additional Example 2B: Using a Step Diagram to Find Prime Factorization
Write the prime factorization of the number.
B. 275
Divide 275 by 5. Write the quotient
below 275. 5
275 5 55 11 11
Stop when the quotient is 1. 1
The prime factorization of 275 is 5 · 5 · 11, or
52 · 11.

16. Insert Lesson Title Here
Try This: Example 4
Write the prime factorization of each number.
A. 324
Divide 324 by 2. Write the
quotient below 324. 2
324 2
162
Keep dividing by a prime
number. 3 81 3 27 3 9
Stop when the quotient is 1. 3 3 1
The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or
22 · 34.

17. Insert Lesson Title Here
Try This: Example 2B
Write the prime factorization of the number.
B. 325
Divide 325 by 5. Write the quotient
below 325. 5
325 5 65 13 13
Stop when the quotient is 1. 1
The prime factorization of 325 is 5 · 5 · 13, or
52 · 13.

18. There is only one prime factorization for any given composite number
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. 2
476 7
476 2
238 2 68 7
119 2 34 17 17 17 17 1 1
The prime factorizations are 2 · 2 · 7 · 17 and
7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.