Greatest common factor
• The greatest common factor (GCF) of
two or more numbers is the greatest
number that is a factor of these
numbers.
To find the greatest common factor
(GCF):
1. List the factors of each number
2. List the common factors of the numbers
3. Find which common factor is the
greatest
First Method
• Find the Greatest Common Factor (GFC)
of 12 and 27.
1. List the factors of each number
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
Factors of 12:
1,2,3,4,6,12
1 x 27 = 27
3 x 9 = 27
factors of 27:
1,3,9,27
2. The common factors are : 1, 3
3. Find which common factor is the greatest
Common factors of 12 and 27: 1, 3
Greatest common factor (GCF) of 12 and 27: 3
Study this example:
Find the greatest common factor
(GCF) of 16, 28, and 32.
1x16 =16
1x28 =28
1x32 =32
2x 8 =16
2x14 =28
2x16 =32
4x 4 =16
4x 7 =28
4x 8 =32
Factors of 16:
1,2,4,8,16
Factors of 28:
1,2,4,7,14,28
Factors of 32:
1,2,4,8,16,32
Common Factors of 16, 28, and 32: 1, 2, 4
Greatest common factor (GCF) of 16, 28, and 32:
4
Here you have more examples:
• Factors of 12 and 6
You can evenly divide 12 by 1, 2, 3, 4, 6 and 12.
You can evenly divide 6 by 1, 2, 3 and 6.
Now look at both sets of numbers. What is the largest
factor of both numbers?
6 is the largest or greatest factor for 12 and 6.
• Factors of 8 and 32
• You can evenly divide 8 by 1, 2, 4 and 8.
You can evenly divide 32 by 1, 2, 4, 8, 16 and 32.
• Therefore the largest common factor of both numbers
is 8.
Multiplying Common PRIME
Factors
• This is another method to find the greatest
common factor.
1. Decompose the numbers in prime factors.
2. select the common factors with the smaller
exponents and multiply them.
Let's take 8 and 32.
1. We decompose the numbers in prime
factors.
8 2
32 2
4 2
16 2
2 2
8 2
1
4 2
2 2
1
2. We select the common factors with the smaller
exponents and we multiply them.
8 2
32 2
4 2
16 2
2 2
8 2
1
4 2
2 2
1
3
The prime factors of 8 are 2 x 2 x 2. (2 )
5
the prime factors of 32 are 2 x 2 x 2 x 2 x 2. (2 )
3
3
5
(2 ) has a smaller exponent than (2 )
(2 ) = 2 x 2 x 2 = 8 which becomes the greatest
common factor.
• Both methods will help you determine
the greatest common factors (GFCs).
However, you will need to decide
which method you prefer to work
with.
Class Activity
• Copy and complete the table.
Number
Factors
6
????
10
????
18
??????
24
????????
Common Factors GCF
??
?
????
?
List the factors of each number. Then
underline the common factors of each
pair of numbers.
1. 6 and 9
3. 4 and 11
5. 11 and 26
7. 8 and 20
2. 3 and 15
4. 10 and 24
6. 8 and 12
8. 10 and 30
• PROBLEM SOLVING
1. Ms. Durkin wants to package 16 math
books and 28 science books equally
without mixing the books and with none
left over. What is the greatest number
of books she can put in each package?
2. Mr. Diaz wants to group the 18 girls and
24 boys at the summer camp separately
into teams. To be able to match boys
with girls during the games , the team
sizes have to be the same . What is the
greatest team size the boys and girls can
form?