Transcript GCF Example: Applying skills that we have learned…

GCF Example: Applying skills
that we have learned…
• Samantha has two pieces of cloth. One
piece is 72 inches wide and the other
piece is 90 inches wide. She wants to cut
both pieces into strips of equal width that
are as wide as possible. How wide should
she cut the strips? How many strips will
she have when she is done?
Samantha has two pieces of cloth. One
piece is 72 inches wide and the other piece
is 90 inches wide. She wants to cut both
pieces into strips of equal width that are as
wide as possible. How wide should she cut
the strips?
• What do I Know: The pieces of cloth are 72 and
90 inches wide.
• What do I need to know: How wide should she
cut the strips so that they are the largest possible
equal widths?
How many strips will she have when she is
done?
Samantha has two pieces of cloth. One
piece is 72 inches wide and the other piece
is 90 inches wide. She wants to cut both
pieces into strips of equal width that are as
wide as possible. How wide should she cut
the strips?
• Plan: This problem can be solved
using Greatest Common Factor
because we are cutting or “dividing”
the strips of cloth into smaller
pieces (factor) of 72 and 90.
• Find the GCF of 72 and 90
GCF Word Problem Solution
List Method:
1 l 72
2 l 36
3 l 24
4 l 18
6 l 12
8l9
1 l 90
2 l 45
3 l 30
5 l 18
6 l 15
9 l 10
Prime Factor Method
72 = 2 x 2 x 2 x 3 x 3
90 = 2 x 3 x 3 x 5
.
GCF = 2 x 3 x 3 = 18
Samantha should cut each piece to be 18 inches wide
How many strips will she have when she is done?
• 72 divided by 18 equals 4
• 90 divided by 18 equals 5
• She will have (4 + 5) or 9 strips that
are 18 inches wide when she is done.
COURSE 3 LESSON 4-1
Factors
A band with 36 members is marching with a 32-member
band. If the two bands are to have the same number of columns,
what is the greatest number of columns in which you could
arrange the two bands?
Begin by finding the factors of 36 and 32.
36:
1, 2, 3, 4, 6, 9, 12, 18, 36
32:
1, 2, 4, 8, 16, 32
The factors 1, 2, and 4 are common to both numbers.
The GCF is 4.
So, 4 is the greatest number of columns in which you can arrange the bands.
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COURSE 3 LESSON 4-1
Factors
Find the GCF of 55 and 231.
Step 1 Find the prime factorization of each number.
55
5
231
11
3
77
7
11
Step 2 Find the product of the common prime factors of each number.
55 = 5 • 11
231 = 3 • 7 • 11
The only common prime factor is 11. The GCF of 55 and 231 is 11.
4-1