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3. Find the prime factorization of a composite number
Objective
Find the prime factorization of a composite number
Example 1-4b

4. Vocabulary Prime number
A whole number greater than 1 that has exactly two factors, 1 and itself
Example 1-4b

5. A whole number greater than 1 that has more than 2 factors
Vocabulary
Composite number
A whole number greater than 1 that has more than 2 factors
Example 1-4b

6. Expressing a composite number as a product of prime numbers
Vocabulary
Prime factorization
Expressing a composite number as a product of prime numbers
Example 1-4b

7. A diagram showing the prime factorization of a number
Vocabulary
Factor tree
A diagram showing the prime factorization of a number
Example 1-4b

8. Two or more numbers that are multiplied together to form a product
Review Vocabulary
Factors
Two or more numbers that are multiplied together to form a product
Example 1-4b

9. Example 1 Identify Numbers as Prime or Composite
Example 3 Find the Prime Factorization
Example 4 Factor an Algebraic Expression
Lesson 1 Contents

10. Determine whether the number 63 is prime or composite.
Write the number 63
All numbers (except 1) has 2 factors: 1 and the number itself
6 + 3 = 9
Determine if any number other than 1 and 63 are factors of 63
9  3 = 3
Remember divisibility rules:
If the sum of the digits is divisible by 3 then the number is divisible by 3
63 is divisible by 3 so is not prime
Answer: Composite
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Example 1-1a

11. Determine whether the number 41 is prime or composite.
Answer: prime
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Example 1-1b

12. Determine whether the number 29 is prime or composite.
Write the number 29
All numbers (except 1) has 2 factors: 1 and the number itself
2 + 9 = 11
Determine if any number other than 1 and 29 are factors of 29
Remember divisibility rules:
If the sum of the digits is divisible by 3 then the number is divisible by 3
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Example 1-2a

13. Determine whether the number 29 is prime or composite.
Remember divisibility rules: 29
11 is not divisible by 3 so 29 is not divisible by 3
2 + 9 = 11
29 is not even so is not divisible by 2
Continue checking divisibility by prime numbers
The one’s digit is not a 0 or 5 so is not divisible by 5
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Example 1-2a

14. Determine whether the number 29 is prime or composite.
Remember divisibility rules: 29
29 is not divisible by 7 because 7  4 = 28
2 + 9 = 11
29 is not divisible by 11 because 11  3 = 33
Since we have checked divisibility past 29 we have confirmed that 29 is a prime number
Answer: Prime
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Example 1-2a

15. Determine whether the number 24 is prime or composite.
Answer: composite
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Example 1-2b

16. Find the prime factorization of 100.
Write number then use factorization ladder
Decide on prime number that will go evenly into 100 2
100 2 50
Can use any prime factor like 2 or 5 5 25 5
Decide on prime number that will go evenly into 50
Decide on prime number that will go evenly into 25
5 is a prime number so you are done prime factoring
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Example 1-3a

17. Find the prime factorization of 100.
Write using prime numbers and exponents 2
100
Write the smallest prime number that was used 2 2 50 5 25
Circle the 2’s that were used 5
2 two’s were used so that is the exponent with the 2 2  2
Put the multiplication sign
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Example 1-3a

18. Find the prime factorization of 100.
Write the next smallest prime number which is 5 2
100
Circle the 5’s that were used 2 50
2 five's were used so that is the exponent with the 2 5 25 5
All prime numbers used have been circled so you are done! 2  2 5 2
Answer: 22  52
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Example 1-3a

19. Find the prime factorization of 72.
Answer: 23  32
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Example 1-3b

20. Write number then use factorization ladder
ALGEBRA Factor
Write number then use factorization ladder 3
21m2n
Decide on prime number that will go evenly into 21 7
7m2n 7
The prime number 3 will divide into 21 evenly
Divide 21 by 3
Bring down m2n
Decide on prime number that will go evenly into 7
The prime number 7 will divide into 7 evenly
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Example 1-4a

21. Divide 7 into 7 then use the Identity Property to multiply 1  m2n
ALGEBRA Factor
Divide 7 into 7 then use the Identity Property to multiply 1  m2n 3
21m2n
Since m2 = m  m, m can be a prime variable 7
7m2n 7 m
m2n
Divide m into m2 which will be m m mn m
Bring down the n
Remember a variable by itself is prime so use m as a prime
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Example 1-4a

22. Divide m into mn which will leave n 3 21m2n 7 7m2n 7
ALGEBRA Factor
Divide m into mn which will leave n 3
21m2n 7
7m2n 7
The variable is a prime and is by itself so you are done prime factoring! m
m2n m mn m n
Now write the answer as factors
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Example 1-4a

23. Write the smallest prime number which is 3 3 21m2n 7 7m2n 7
ALGEBRA Factor
Write the smallest prime number which is 3 3
21m2n 7
7m2n 7
Circle the 3 m
m2n
Since the direction say “factor” then do not use exponents m m mn n
Put the multiplication sign
Circle the next factor which is 7 and write it down
3  7
3  3 
Put the multiplication sign
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Example 1-4a

24. Circle the next factor which is m and write it down 3 21m2n 7 7m2n 7
ALGEBRA Factor
Circle the next factor which is m and write it down 3
21m2n 7
7m2n 7
Put the multiplication sign m
m2n
Circle the next factor which is m and write it down m m mn n
Put the multiplication sign
Answer:
Circle the next factor which is n and write it down
3  7 
m  m 
m  m  n
m 
m  m m
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Example 1-4a

25. *
ALGEBRA Factor
Answer:
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Example 1-4b

26. Assignment
Lesson 5:1
Prime Factorization
All
End of Lesson 1