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Greatest Common Factor
for
Visual Learners
Fortner
Common Core Standard
Compute fluently with multi-digit numbers and find common
factors and multiples.
CC.6.NS.4
Find the greatest common factor of two whole numbers less than or equal
to 100 and the least common multiple of two whole numbers less than or
equal to 12. use the distributive property to express a sum of two whole
numbers with no common factor.
Lesson Objective
Find the greatest common factor
of two whole numbers.
ESSENTIAL QUESTION:
How can you find the greatest common factor of
two whole numbers?
VOCABULARY:
COMMON FACTOR: a number that is a factor of two or more numbers.
GREATEST COMMON FACTOR: (GCF) the greatest factor that two
or more numbers have in common.
Problem of the Day
TEST PREP:
A group of students are helping pass out fliers for a bake sale.
They have 1,500 fliers to pass out. If they want to pass out
all of the fliers in 3 hours, how many fliers do they need to pass
out each hour?
A
5, 000
C
50
B
500
D
5
Greatest Common Factor
A common factor is a number that is a factor of two or more numbers.
The numbers 16 and 20 have 1, 2, and 4 as common factors.
FACTORS OF 16 : 1, 2, 4,
FACTORS OF 20: 1, 2, 4, 5,
8,
16
10,
20
The GREATEST COMMON FACTOR (GCF) is the greatest factor that two
Or more numbers have in common.
The GREATEST COMMON FACTOR or GCF of
16 and 20 is 4.
REMEMBER
A number that is multiplied by another number to find a
product is a factor.
Factors of 6: 1, 2, 3, 6
Factors of 9: 1, 3, 9
Every number has 1 as a factor.
Unlock the Problem
Jim is cutting two strips of wood to make picture frames.
The wood strips measure 12 inches and 18 inches. He wants
To cut the strips into equal lengths that are as long as possible.
Into what lengths should he cut the wood?
Find the greatest common factor, or GCF
of 12 and 18.
One Way:
Use a list
FACTORS OF 12 : 1, 2, ___,
3 ___,
4 ___,
6 12
FACTORS OF 18: 1, ___,
2 ___,
3 ___,
6 ___,
9 ___
18
The GREATEST COMMON FACTOR, or (GCF), is ____
6
MATH
TALK
Into what other lengths could Jim
cut the wood
to obtain equal lengths?
1- inch, 2- inch, or 3-inch lengths
Another Way:
Use Prime Factorization.
Write the prime factorization of each number.
12 = 2 x ____
2 x3
2 x 3 x ____
3
18 = ____
Place the prime factors of the
Numbers in the appropriate parts
Of the Venn Diagram
Prime factors of 12
2
2
3
Prime factors of 18
3
Common Prime Factors
To find the GCF, find the product of
the common prime factors.
2 x 3 = 6 The GCF is 6
So, Jim should cut the wood into _____
6 -inch lengths.
Distributive Property
Multiplying a sum by a number is the same as
multiplying each addend by the number and
then adding the products.
5 x (8 + 6) = (5 x 8) + (5 x 6)
You can use the Distributive Property
to express the sum of two whole
numbers as a product if the numbers
have a common factor.
Example:
Use the GCF and the Distributive Property to express
36 + 27 as a product.
Find the GCF of 36 and 27
Write each number as the product
of the GCF and another factor.
9
GCF: ______
36 + 27
3
4 + (9 x ____)
(9 x ___)
Use the Distributive Property to
Write 36 + 27 as a product.
Check your answer.
9 x (4 + ___)
3
63
36 + 27 = _____
9 x (4 + ___)
3 = 9 x ___
7 = ___
63
9 x (___
4 + ___).
3
So, 36 + 27 = ___
1. Explain two ways to find the GCF of 36 and 27.
List the factors of each number and circle the GCF.
Another Way: Write the prime factorization
of each number and find the product of the
common prime factors.
2.
Describe how the figure at the right shows that
36 + 27 = 9 x (4 + 3 )
The model shows an array with
36 + 27 = 63 squares. The array
has 9 rows and is divided into
two parts, one part with 4 columns
9
and one part with 3 columns.
So, the model shows 9 rows of
4 columns plus 3 columns, or
9 x (4 + 3) squares
4
3
9x4
9x3
Share and Show
1. List the factors of 12 and 20. Circle the GCF
FACTORS OF 12 : ___,___,
1 2 ___,
3 ___,
4 ___,
6 ___
12
1 2 ___,
4 ___,
5 ___,
10 ___
20
FACTORS OF 20: ___,___,
Find the GCF.
2. 16, 18 3. 25, 40
2
5
4.
24, 40 5. 14, 35
8
7
Use the GCF and the Distributive Property to express the sum as a product.
6. 21 + 28
7. 15 + 27
7 x (3 + 4)
3 x (5 + 9)
MATH TALK
8. 40 + 15 9. 32 + 20
5 x (8 + 3)
4 x (8 + 5)
Explain how to use the prime factorization
of two numbers to find their GCF.
Write the prime factorization of each
number. Then find the prime factors
that are common to the two numbers.
The GCF is the product of the
common prime factors.
On Your Own
Find the GCF.
10. 8, 12
4
11. 27, 45
9
12. 30, 45 13. 42, 63
15
21
14. 8, 25 15. 31, 32 16. 56, 64 17. 150, 275
1
1
8
25
Use the GCF and the Distributive Property to express the sum as a product.
18. 24 + 30 19. 49 + 14 20. 40 + 15 21. 60 + 12
6 x (4 + 5)
7 x (7 + 2)
9 x (7 + 9)
12 x (5 + 1)
Problem Solving
Use the table for 22 – 25. Teachers at the Scott School of Strings
Teach only one instrument in each class.
Scott School of Strings
Instrument
Number of students
Bass
20
Cello
27
Viola
30
Violin
36
Scott School of Strings
Instrument
Number of students
Bass
20
Cello
27
Viola
30
Violin
36
22. Francisco teaches group lessons to all of the violin and viola
Students at the Scott School of Strings. All of his classes have the
same number of students. What is the greatest number of
students he can have in class?
6
Scott School of Strings
Instrument
Number of students
Bass
20
Cello
27
Viola
30
Violin
36
23. Amanda teaches music history lessons to all of the cello, viola, and
violin students. All her classes have the same number of students. What is the
greatest number of students she can have in each class?
3
Scott School of Strings
Instrument
Number of students
Bass
20
Cello
27
Viola
30
Violin
36
24. Mila teaches jazz classes. She has 9 students in each class, and she teaches a
all the students who play two instruments. How many students does she have,
and which two instruments does she teach?
63; cello and violin
Scott School of Strings
Instrument
Number of students
Bass
20
Cello
27
Viola
30
Violin
36
25. WRITE MATH: Explain how you could use the GCF and the Distributive
Property to express the sum of the number of bass students and the number
of violin students as a product.
Find the GCF of 20 and 36: 4
Then write 20 and 30 as a product
of 4 and another factor. Finally,
use the Distributive Property to
write 20 + 36 as a product: 4 x (5 + 9)
Test Prep
26. Tina has 3 ribbons measuring 18 inches, 24 inches, and 36 inches.
She wants to cut them into equal pieces that are as long as possible.
Into what lengths should she cut the ribbons?
A
3 inches
C
6 inches
B
4 inches
D
12 inches
VOCABULARY:
Common factor: a number that is a factor of two or more numbers.
Greatest common factor (GCF): the greatest factor that two
or more numbers have in common.
Least common multiple (LCM): the least number that is a common
Multiple of two or more numbers.
Prime factorization: a number written as the product of all its prime
factors.
Compatible numbers: numbers that are easy to compute with mentally.
VOCABULARY:
Decimal: a number with one or more digits to the right of the decimal point.
Dividend: the number that is to be divided in a division problem.
Divisor: the number that divides the dividend.
Prime numbers: a number that has exactly two factors, one and itself.
Quotient: the number, not including the remainder, that results from dividing.