Download 4.4 (AVID) Prime Factorization.notebook

4.4 (AVID) Prime Factorization.notebook
Warm­up 10/30/12
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Is it possible to write the numbers:
30
75
180
as products using only the factors 2,3 and 5?
If so, how?
October 29, 2012
Prime Factorization
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Prime numbers: have exactly two factors ­ 1 and itself.
Example: 3­ factors are 1 and 3 Composite numbers: have more than 2 factors.
Example: 8 ­ factors are 1, 2, 4, 8
• Numbers 1 and 0 are neither prime nor composite, why?
• 2 is the only prime number that is even.
Writing Prime Factorization (Factor Trees)
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All composite numbers can be written as product of prime numbers.
Example: Prime factorization of 60.
You Try:
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Write the prime factorization of 72 and ­36 .
72
­36
Step 1: Start with any factors of 60.
60
Step 2: Continue to break down all factors until all prime numbers are left.
Step 3: List all primes as products or use exponents for duplicate primes.
Writing Prime Factorization (Cake Method)
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Step 1: Divide by smallest
prime number that is a factor of dividend.
Step 2: Repeat, divide quotient
by smallest prime factor.
Step 3: Repeat until quotient is prime.
Factoring Monomials
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Monomials can also be written in factorial form as product of prime numbers, ­1, and no exponent greater than 1.
Example: 28x2y
210
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4.4 (AVID) Prime Factorization.notebook
October 29, 2012
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Finding the Greatest Common Factor
2
1. 42xy
Greatest Common Factor (GCF) is the greatest factor in common of all numbers.
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You Try:
3
2. 21xy
Example find the GCF of 24 and 36.
2 4
Method 1 ­ Listing Factors
Step 1: List all factors of both numbers
Factors of 24:
Factors of 36:
Step 2: Identify greatest common factor.
3. 75m k
*This method not best for large numbers with a lot of factors.
Method 2 ­ Prime Factorization (Factor Tree)
Step 1: Write Prime Factorization of both numbers.
36
24
Step 2: Find product of all common factors.
*If two same factors repeat multiply them that number of times.
24: 2 x 2 x 2 x 3 2 x 2 x 3 = 12
36: 2 x 2 x 3 x 3
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Finding the GCF of Monomials
You can use either Method 1 or 2
Example: GCF of 36x3y and 56xy2
Method 1: List all factors of each #.
Step 1: List factors.
36x3y:
56xy2:
You Try:
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Find the GCF of each set.
A. 32mn2, 16n, 12n3
B. 18a, 30ab, 42b
Step 2: Identify GCF and shared variables.
*Both monomials must share variable in order to factor out to GCF.
Method 2 ­ Prime Factorization
Step 1: Write Prime Factorization for each #.
36x3y
56xy2
Step 2: Find product of shared prime factors and variables.
Factoring Expressions
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Ex. 8v + 56
Step 1: Identify GCF
Homework: Workbook pg. 23 odds & 24 odds
Step 2: Factor (divide) GCF out of each term
8v + 56; GCF is 8
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4.4 (AVID) Prime Factorization.notebook
October 29, 2012
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