How many squares can you
count?
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Rosa is making a game board that is
16 inches by 24 inches. She wants to
use square tiles. What is the largest
tile she can use?
GCF Problem Solving
First, use the KWL method for
approaching all problems…



K:
W:
L:
What do you know?
What do you want to know
What did you learn?
If it is a GCF Problem
(Greatest Common Factor)
What is the question asking us?
 Do we have to split things into smaller
sections?
 Are we trying to figure out how many
people we can invite?
 Are we trying to arrange something
into rows or groups?

GCF Example: Applying
what 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?
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?
K: The pieces of cloth are 72 and 90
inches wide.
 W: How wide should she cut the strips
so that they are the largest possible
equal lengths.
 Draw a picture of what this looks like to
you.

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?
L: 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
2 l 72
2 l 36
2 l 18
3l9
3l3
1
2 l 90
3 l 45
3 l 15
5l5
1
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
Question #1
Mrs. Evans has 120 crayons and 30
pieces of paper to give to her
students. What is the largest # of
students she can have in her class so
that each student gets equal # of
crayons and equal # of paper.
Question #3
I am planting 50 apple
trees and 30 peach
trees. I want the same
number and type of
trees per row. What is
the maximum number
of trees I can plant per
row?
Homework Problems
You made 63 wheat dinner rolls, 45 rye
dinner rolls, and 54 sourdough dinner rolls for
a family picnic. You want to make up plates of
rolls to set on the picnic tables. If each plate
is to contain the same amount of each type of
roll, and there are no left over rolls, what is
the greatest number of plates that can be
made? How many wheat dinner rolls, rye
dinner rolls, and sourdough dinner rolls are
there on each plate?
Rebecca has 20 table tennis balls
and 16 table tennis paddles. She
wants to sell packages of balls and
paddles bundled together. What is
the greatest number of packages
she can sell with no leftover balls
or paddles?
Indira has two pieces of ribbon,
one 20 inches long and the other 8
inches long. To decorate an album,
she wants to cut them up to
produce many pieces of ribbon that
are all of the same length, with no
ribbon left over. What is the
greatest length, in inches, that she
can make them?
Wakaki has 50 cans of soda and
45 bottles of water. In preparation
for the intermission of the school
play, Wakaki wants to set up
identical refreshment tables, with
no beverages left over. What is the
greatest number of refreshment
tables that he can set up?