prime factorization
DESCRIPTION
Educational slides to understand teh concepts of prime numbers and composite numbers.TRANSCRIPT
2-4 Prime Factorization
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpWrite each number as a product of two whole numbers in as many ways as possible.
1. 6
2. 16
3. 17
4. 36
5. 23
1 · 6, 2 · 3
1 · 16, 2 · 8, 4 · 4
1 · 17
Course 2
2-4 Prime Factorization
1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6
1 · 23
Problem of the Day
Nicholas bikes every third day and skates every other day. Today is April 5, and Nicholas biked and skated. On what date will he both bike and skate?April 11
Course 2
2-4 Prime Factorization
Learn to find the prime factorizations of composite numbers.
Course 2
2-4 Prime Factorization
Vocabulary
prime numbercomposite numberprime factorization
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Course 2
2-4 Prime Factorization
Course 2
2-4 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
2-4 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.
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.
Write the prime factorization of the number.
Additional Example 1A: Using a Factor Tree to Find Prime Factorization
Course 2
2-4 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.
Additional Example B: Using a Factor Tree to Find Prime Factorization
Course 2
2-4 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
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Course 2
2-4 Prime Factorization
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
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Course 2
2-4 Prime Factorization
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.
Course 2
2-4 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. The prime factors are the number are the prime numbers you divided by.
Write the prime factorization of each number.
Additional Example 2A: Using a Step Diagram to Find Prime Factorization
Course 2
2-4 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
Course 2
2-4 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 2A
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Course 2
2-4 Prime Factorization
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
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Course 2
2-4 Prime Factorization
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.
Course 2
2-4 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 QuizUse a factor tree to find the prime factorization.
1. 27
2. 36
3. 28
Use a step diagram to find the prime
factorization.
4. 132
5. 52
6. 108
22 · 32
33
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22 · 7
22 · 3 · 11
Course 2
2-4 Prime Factorization
22 · 1322 · 33