Greatest Common
Factor (GCF)
Created by: Mrs. J Couch
GCF
 Finding the greatest of the common factors of two (or
more) numbers
Example
 Find the GCF of 20 and 24 using prime factorization.
20 = 2 x 2 x 5
24 = 2 x 2 x 2 x 3
-Identify all common factors in the factorization of 20 and
24.
20 = 2 x 2 x 5
24 = 2 x 2 x 2 x 3
The greatest common factor of 20 and 24 is the product of
all common factors 2 x 2 = 4
Finding GCF using
Ladder Method
Divide out all the common factors down the left side.
GCF= 2 * 2 * 3 = 12
What number
(smallest prime #)
goes into both
Does
#
24
andany
60?
besides 1
go into both
How about
12 and 30?
6 and 15?
Anything else?
No?
You’re done.
Multiply left side
Only to get GCF
Practice
 Find the greatest common factor of 24 and 18.
Practice
 Find the greatest common factor of 96 and 72.
Practice
 Find the greatest common factor of 32 and 52.
Practice
 Xavier is visiting the hospital in order to give stuffed
animals and books to sick children. He has 16 stuffed
animals and 20 books to give. If he wants to give the
same combination of stuffed animals and books to
each child, with no gifts left over, what is the greatest
number of children Xavier can give gifts to?
(Remember to give your answer using a complete
sentence)
Practice
 Find the GCF of 12 and 36
Practice
 Two students are having a party. They want to make
treat bags for their guests. They want each bag to be
identical with nothing leftover. They have 36 Silly Bandz
and 72 pieces of bubble gum to put in the bags. What
is the greatest number of treat bags they can make and
how many of each item will be in each treat bag?
Practice
 Mitzi is making trail mix out of 48 bags of nuts and 32
bags of dried cranberries. She wants each new portion
of trail mix to be identical containing the same
combination of nuts and cranberries with nothing left
over. What is the greatest number of portions of trail
mix Mitzi can make and how much of each ingredient
will be in each portion?
Connection to Distributive
Property
 How does finding the greatest common factor help you
in the distributive property?
Ex.
Write a number sentence for 12 + 18
-think about the common factors of 12 and 18
Common factors: 1, 2, 3, 6
2 (6 + 9)
Use the common factors to write the
number sentence
3(
+
)
6(
+
)
Practice with
Distributive Property
 Write a number sentence (using the GCF) for:
 42 + 36
 18 + 25
 50 + 60
Exit Slip
 Find the GCF of 27 and 36
 Find the GCF of 12 and 22
 Find the GCF of 42 and 80
 Write a number sentence (using the GCF) for 20 + 25