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Name ———————————————————————
LESSON
Date ————————————
/ZMI\M[\+WUUWV.IK\WZ
California
Standards
Gr. 6 NS 2.4: Determine
the least common
multiple and the
greatest common
divisor of whole
numbers; use them to
solve problems with
fractions (e.g., to find a
common denominator
to add two fractions or
to find the reduced form
for a fraction).
Words to Remember
Common factors of 8 and 12
Common factor: Any whole number that is a
factor of two or more non-zero whole numbers
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Greatest common factor (GCF): The largest
whole number that is a factor of two or
more non-zero whole numbers
Greatest common factor of 8 and 12
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Getting Started In Lesson 2-1 you learned how to find the factors of a
number. You can also use the factors of two or more numbers to find the
greatest common factor (GCF).
E@)584-
Finding Common Factors
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Find all the common factors of 20 and 30.
Solution
;\MX List all the factors of 20 and 30.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
;\MX Circle the factors that appear in both lists.
Factors of 20: 1 , 2 , 4, 5 , 10 , 20
Factors of 30: 1 , 2 , 3, 5 , 6, 10 , 15, 30
ANSWER The common factors of 20 and 30 are 1, 2, 5, and 10.
T:A <0 1;
1.
2.
14 and 34
Find all the common factors of the numbers.
Factors of 14:
,
, 7,
__________ Factors of 34:
,
,
28 and 72
Factors of 28: 1, 2,
__________ Factors of 72:
6
Math Intervention
Book 2 Fractions and Decimals
,
, 34
,
,
,
,
,
, 6,
,
, 12,
,
,
,
Name ———————————————————————
3FQFBUFE'BDUPST
When a factor
repeats, you only list
it once. For example,
for the factors of 36,
only list the 6 once.
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Date ————————————
Finding the GCF Using a List
Find the greatest common factor of 36 and 48.
Solution
;\MX List all the factors of 36 and 48.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
;\MX Identify and circle the greatest factor that appears in both lists.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
ANSWER The GCF of 36 and 48 is 12.
T:A <0 1;
3.
Make a list to find the GCF.
16 and 24
4.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
E@)584-
9 and 27
Finding the GCF Using Prime Factorization
Find the greatest common factor of 98 and 70.
Solution
Write the prime factorizations of 98 and 70.
98
70
2 3 49
14 3 5
2 3 7 3 7
2 3 7 3 5
Circle all the common prime factors.
The common prime factors are 2 and 7. The GCF is the product of the
common prime factors.
ANSWER The GCF of 98 and 70 is 2 3 7, or 14.
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5.
Use prime factorization to find the GCF.
52 and 96
52
6.
96
126 and 210
26
1
21
0
Math Intervention
Book 2 Fractions and Decimals
7
Name ———————————————————————
Summarize
Date ————————————
63: 1, 3, 7, 9, 21 , 63
GCF is 21.
Finding the GCF Using a List
42: 1, 2, 3, 6, 7, 14, 21 , 42
List all the factors of the numbers. Identify the
greatest factor that appears in each list.
63
42
7 3 9
6 3 7
7 3 3 3 3
2 3 3 3 7
Finding the GCF Using
Prime Factorization
Write the prime factorization of the numbers.
Identify all the common prime factors.
Multiply them together to find the GCF.
GCF is 7 3 3 5 21.
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Fill in the missing information to find all the common factors of
the numbers.
6 and 8
2.
Factors of 6:
,
,
,
Factors of 9:
Factors of 8:
,
,
,
Factors of 18:
____________
3.
9 and 18
,
,
,
,
,
24 and 38
4.
21 and 49
Factors of 21:
,
,
,
Factors of 49:
,
,
30 and 75
____________
Make a list to find the greatest common factor of the numbers.
4 and 74
Factors of 4:
6.
,
Factors of 74:
,
,
,
,
GCF: ____________
7.
56 and 64
GCF: ____________
8.
GCF: ____________
15 and 105
GCF: ____________
Use prime factorization to find the greatest common factor of the numbers.
9.
16 and 72
6
1
10.
72
45 and 120
GCF: __________
8
Math Intervention
Book 2 Fractions and Decimals
60 and 90
60
GCF: __________
11.
,
____________
____________
5.
,
90
GCF: __________
12.
100 and 180
GCF: __________
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
1.
Name ———————————————————————
Date ————————————
First tell whether you will find common factors or the greatest common
factor. Then solve the problem. Explain your reasoning.
13. Ms. Randolf wants to divide Mr. Hunt’s class of 14 students and
Ms. Cary’s class of 21 students into smaller groups of equal size.
She does not want to mix the classes. What is the greatest number
of students that she can put in one group?
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14. You have 30 apples and 40 pears. You are
dividing the fruit into equal groups without
mixing types of fruit. Name all possible
group sizes. The groups must have more
than one piece of fruit.
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Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
15. You have 220 black-and-white photos and 400 color photos to
display on posters. You want to put the same number of photos
on each poster without mixing black-and-white photos with color
photos. What is the greatest number of photos you can put on each
poster?
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16. Fill in the missing words. To find the GCF using prime
factorization, determine the __________ of all the common
prime factors.
17. Work backwards. The GCF of two numbers is 6. What could
the numbers be? Explain.
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__________________________________________________________________________
Math Intervention
Book 2 Fractions and Decimals
9