Download Algebra 7_1 study guide Factors and Greatest Common Factors

Algebra: 7-1 Study Guide Factors and Greatest Common Factors (pp 456-458)
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Attendance Questions.
Match each term on the left with a definition on the right.
Term
1. ____ Binomial
2. _____ Composite number
3. _____ Factor
4. _____ Multiple
5. _____ Prime number
Definition
A) A whole number greater than 1 that has more than two
positive factors
B) A polynomial with two terms
C) The product of any number and a whole number
D) A number that is written as the product of its prime
factors
E) A whole number greater than 1 that has exactly two
positive factors, itself and 1
F) a number that is multiplied by another number to get
a product
6. Write the first four multiples of 15.
7. Is 7 a factor of 245? Explain why or why not.
Algebra: 7-1 Study Guide Factors and Greatest Common Factors (pp 456-458)
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Tell whether each number is prime or composite. If the number is composite, write
it as the product of two numbers.
8. 151
Multiply.
(
9. 93
)
10. 6m m 2 − 4m − 1 11. (b- 7)(b+ 1) 12. (3n+ 4)(2n+ 3)
• I can write the prime factorization of numbers.
• I can find the GCF of monomials.
Common Core: CC.9-12.A.SSE.2 Use the structure of an expression to identify ways to rewrite
it. For example, see x4–y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can
be factored as (x2 – y2) (x2 + y2).
13. What is the factor of a number?
14. What is the fundamental theorem of arithmetic?
Algebra: 7-1 Study Guide Factors and Greatest Common Factors (pp 456-458)
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Remember!
A prime number has exactly two factors, itself
and 1. The number 1 is not prime because it only
has one factor.
Example 1: Refer to lesson tutorial example 1 to complete the following question.
Use the tree diagram and the ladder diagram to prime factorize 80.
Guided Practice: Prime factorize the following numbers.
15. 40
16. 33
19.What is the greatest common factor?
17. 49
18. 19
Algebra: 7-1 Study Guide Factors and Greatest Common Factors (pp 456-458)
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Example 2: Refer to lesson tutorial example 2 to complete the following
questions.
A) List the factor of 45 and 60 to find the GCF .
B) Use prime factorization to find the GCF of 24 and 36.
Guided Practice: Find the GCF of the following pairs of numbers.
20. 12 and 16 21. 15 and 25
Example 3: Find the GCF of the following monomials.
A. 8x & 4x 2 B. 3a 2 & 5b 4
Helpful Hint
If two terms contain the same variable raised to
different powers, the GCF will contain that
variable raised to the lower power.
Algebra: 7-1 Study Guide Factors and Greatest Common Factors (pp 456-458)
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Guided Practice. Find the GCF of the following pairs of numbers
22. 18g 2 & 27g 3 23. 16a 6 & 9b 25. 8x & 9v 2
Example 4: Morgan is hanging framed photographs by Ansel Adams and 12
photographs by Dorothea Lange. The photos will be displayed in rows along a
large wall with the same number in each row. How many rows will be there be if
Morgan puts the greatest possible number of photographs in each row?
Algebra: 7-1 Study Guide Factors and Greatest Common Factors (pp 456-458)
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27. Guided Practice: Adrianne is shopping for a CD storage unit. She has 36 CDs
by pop music artists and 48 CDs by country music artists. She wants to put the
same number of CDs on each shelf without putting pop music and country music
CDs on the same shelf. If Adrianne puts the greatest possible number of CDs on
each shelf, how many shelves does her storage unit need?
7-1 Assignment (pp 459-461) 20, 26, 30, 31, 32, 36, 37, 42, 46, 48, 54, 56-58.