Transcript Prime Factorization

Chapter 2
Multiplying and
Dividing Fractions
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2.2
Factors and Prime
Factorization
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Finding the Factors of Numbers
To perform many operations, it is necessary to be able to
factor a number.
Since 7 · 9 = 63, both 7 and 9 are factors of 63, and 7 · 9 is
called a factorization of 63.
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Prime and Composite Numbers
Prime Numbers
A prime number is a natural number that has
exactly two different factors 1 and itself.
Composite Numbers
A composite number is any natural number, other
than 1, that is not prime.
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Examples
Determine whether each number is prime or composite.
Explain your answers.
a. 16
Composite, it has more than two factors: 1, 2, 4, 8, 16.
b. 31
Prime, its only factors are 1 and 31.
c. 49
Composite, it has more than two factors: 1, 7, 49.
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Prime Factorization
Prime Factorization
The prime factorization of a number is the
factorization in which all the factors are prime
numbers.
Every whole number greater than 1 has exactly one
prime factorization.
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Examples
Find the prime factorization of 63.
The first prime number 2 does not divide evenly, but 3 does.
21
3 63
Because 21 is not prime, we divide again.
7
3 21
3 63
The quotient 7 is prime, so we are finished. The prime
factorization of 63 is 3 · 3 · 7.
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Divisibility Tests
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Factor Trees
Another way to find the prime factorization is to use
a factor tree.
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Examples
Find the prime factorization of 30.
Write 30 as the product of two numbers. Continue until all
factors are prime.
30
6
3
• 2
•
5
• 5
The prime factorization of 30 is 2 · 3 · 5.
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Examples
Find the prime factorization of 36.
Write 36 as the product of two numbers. Continue until all
factors are prime.
36
9
3
• 3
•
4
2 • 2
The prime factorization of 36 is 3 · 3 · 2 · 2 or 32 · 22.
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