2-6 prime factorization course 2 warm up warm up problem of the day problem of the day lesson...
TRANSCRIPT
2-6 Prime Factorization
Course 2
Warm Up
Problem of the Day
Lesson Presentation
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
Course 2
2-6 Prime Factorization
1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6
NOW..
• TURN TO THE NOTES section of your binder. I should see everyone’s note section as I pass around your note sheet.
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
Course 2
2-6 Prime Factorization
Learn to find the prime factorizations of composite numbers.
Course 2
2-6 Prime Factorization
Vocabulary
prime numbercomposite numberprime factorization
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Course 2
2-6 Prime Factorization
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.
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.
Tell whether each number is prime or composite.
Additional Example 1: Identifying Prime and Composite Numbers
Course 2
2-6 Prime Factorization
A. 11
11 is prime.
The factors of 11 are 1 and 11.
B. 16
16 is composite.
The factors of 16 are 1, 2, 4, 8, and 16.
Tell whether each number is prime or composite.
Check It Out: Example 1
Course 2
2-6 Prime Factorization
A. 14
14 is composite.
The factors of 14 are 1, 2, 7, and 14.
B. 7
7 is prime.
The factors of 7 are 1 and 7.
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.
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
Write the prime factorization of each number.
Additional Example 2A: Using a Factor Tree to Find Prime Factorization
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2-6 Prime Factorization
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 or 23 · 3.
Write the prime factorization of each number.
Additional Example 2B: Using a Factor Tree to Find Prime Factorization
Course 2
2-6 Prime Factorization
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.
Check It Out: Example 2A
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Course 2
2-6 Prime Factorization
Write the prime factorization of each number.
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 or 22 · 32.
Check It Out: Example 2B
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Course 2
2-6 Prime Factorization
Write the prime factorization of the number.
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.
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.
Write the prime factorization of each number.
Additional Example 3A: Using a Step Diagram to Find Prime Factorization
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2-6 Prime Factorization
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 3B: Using a Step Diagram to Find Prime Factorization
Course 2
2-6 Prime Factorization
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.
Check It Out: Example 3A
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Course 2
2-6 Prime Factorization
Write the prime factorization of each number.
324
32416281
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
Check It Out: Example 3B
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2-6 Prime Factorization
Write the prime factorization of the number.
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.
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.
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.
Lesson Quiz: Part I
Tell whether each number is prime or composite.
1. 23
2. 39
3. 27
composite
prime
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composite
Course 2
2-6 Prime Factorization
Lesson Quiz: Part II
Write the prime factorization of each number.
4. 27
5. 36
6. 28
7. 132
8. 52
9. 108
22 · 32
33
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22 · 7
22 · 3 · 11
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2-6 Prime Factorization
22 · 1322 · 33