1. 2-6 Prime Factorization Warm Up Problem of the Day Lesson Presentation
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 2-6 Prime Factorization Warm Up: 1. 6 2. 16 3. 17 4. 36 1 · 6, 2 · 3
Course 2
2-6
Prime Factorization
Warm Up:
Write your HW in your agenda.
Get your new math warm up sheet from the red basket in the front of the room.
Turn to you warm up section and put it in THEN begin to answer the questions.
Write each number as a product of two whole numbers in as many ways as possible.
1. 6
2. 16
3. 17
4. 36
1 · 6, 2 · 3
1 · 16, 2 · 8, 4 · 4
1 · 17
1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6

3. NOW..
TURN TO THE NOTES section of your binder. I should see everyone’s note section as I pass around your note sheet.

4. 2-6 Prime Factorization Problem of the Day
Course 2
2-6
Prime Factorization
Problem of the Day
Nicholas bikes every third day and skates every other day. On April 5 Nicholas biked and skated. When will he do both again?
April 11

5. Course 2
2-6
Prime Factorization
Learn to find the prime factorizations of composite numbers.

6. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Vocabulary
prime number
composite number
prime factorization

7. Course 2
2-6
Prime Factorization
In June 1999, Nayan Hajratwala discovered the first known prime number with more than one million digits. The new prime number, 26,972,593 – 1, has 2,098,960 digits.
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.

8. Course 2
2-6
Prime Factorization
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.

9. Additional Example 1: Identifying Prime and Composite Numbers
Course 2
2-6
Prime Factorization
Additional Example 1: Identifying Prime and Composite Numbers
Tell whether each number is prime or composite.
A. 11
B. 16
The factors of 11 are 1 and 11.
The factors of 16 are 1, 2, 4, 8, and 16.
11 is prime.
16 is composite.

10. 2-6 Prime Factorization Check It Out: Example 1
Course 2
2-6
Prime Factorization
Check It Out: Example 1
Tell whether each number is prime or composite.
A. 14
B. 7
The factors of 14 are 1, 2, 7, and 14.
The factors of 7 are 1 and 7.
14 is composite.
7 is prime.

11. Course 2
2-6
Prime Factorization
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.

12. 2-6 Prime Factorization Writing Math
Course 2
2-6
Prime Factorization
You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.
Writing Math

13. Additional Example 2A: Using a Factor Tree to Find Prime Factorization
Course 2
2-6
Prime Factorization
Additional Example 2A: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of each number. 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 or 23 · 3.

14. Additional Example 2B: Using a Factor Tree to Find Prime Factorization
Course 2
2-6
Prime Factorization
Additional Example 2B: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of each number.
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.

15. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Check It Out: Example 2A
Write the prime factorization of each number. 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 or 22 · 32.

16. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Check It Out: Example 2B
Write the prime factorization of the number. 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.

17. Course 2
2-6
Prime Factorization
You can also use a step diagram to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.

18. Course 2
2-6
Prime Factorization
Additional Example 3A: Using a Step Diagram to Find Prime Factorization
Write the prime factorization of each number.
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.

19. Course 2
2-6
Prime Factorization
Additional Example 3B: Using a Step Diagram to Find Prime Factorization
Write the prime factorization of the number.
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.

20. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Check It Out: Example 3A
Write the prime factorization of each number.
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.

21. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Check It Out: Example 3B
Write the prime factorization of the number.
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.

22. Course 2
2-6
Prime Factorization
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.

23. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Lesson Quiz: Part I
Tell whether each number is prime or composite.
1. 23
2. 39
3. 27
prime
composite
composite

24. Insert Lesson Title Here
Course 2
2-6
Prime Factorization
Insert Lesson Title Here
Lesson Quiz: Part II
Write the prime factorization of each number.
4. 27
5. 36
6. 28
7. 132
8. 52
9. 108 33
22 · 32
22 · 7
22 · 3 · 11
22 · 13
22 · 33