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Tallahassee Community College
GREATEST COMMON FACTOR
Use your math book with this lab
STUDY THIS LAB VERY CAREFULLY!
I.
Factors
1.
2.
3.
4.
5.
6.
7.
8.
Factors of 12 are also the _______________ of 12.
Name all of the factors of 12___________________
Name all of the factors of 18___________________
What factors are in both lists?_________________
(These are the common factors of 12 and 18.)
What is the smallest number you listed in #4?________
What is the largest number you listed in #4?_________
6 is called the__________ __________ __________ of 12
and 18.
What does GCF stand for?_____________________________
Listing all the factors of each number and then finding the largest
factor that they share is one way of finding the GCF of the numbers.
Although it is not always the easiest way, it does help you to understand
GCF.
Find the GCF of these numbers by using lists of all the factors of each
number.
II.
9.
Find the GCF of 48 and 64.
10.
Find the GCF of 24, 36 and 42.
Using Prime Factorizations to Find the Greatest Common Factor of Numbers
(1) Write the prime factorization of each number.
(2) The GCF of the numbers is the product of the common prime factors.
EXAMPLE 1:
Find the GCF of 48 and 64
48 = 2 • 2 • 2 • 2 • 3
64 = 2 • 2 • 2 • 2 • 2 • 2
GCF = 2 • 2 • 2 • 2
= 16
1
NOTICE 16 is a factor of 48. It is also a factor of 64.
largest factor shared by 48 and 64.
EXAMPLE 2:
Find the GCF of 24, 36 and 42.
24 = 2 • 2 • 2 • 3
It is the
36 = 2 • 2 • 3 • 3
42 = 2 • 3 • 7
GCF = 2 • 3 = 6
EXAMPLE 3:
Find the GCF of 9 and 54.
9 = 3 • 3
54 = 2 • 3 • 3 • 3
GCF = 3 • 3 = 9
EXAMPLE 4:
(This is a SPECIAL CASE.)
Find the GCF of 9 and 10.
9 = 3 • 3
10 = 2 • 5
GCF = 1
There are no common prime factors, but 1
is a factor of every natural number!
Finding the GCF will be very easy for you if you:
1.
2.
3.
Know what it means
Can find it using prime factorizations
Practice finding the GCF
Find the GCF using prime factorizations.
1.
Find the GCF of 28 and 21.
2.
Find the GCF of 84 and 72.
3.
Find the GCF of 4, 18 and 9.
4.
Find the GCF of 26, 39 and 52.
5.
Find the GCF of 15 and 45.
6.
Find the GCF of 30 and 49.
ANSWERS:
I.
1.
2.
3.
4.
5.
6.
7.
divisors
1, 2, 3,
1, 2, 3,
1, 2, 3,
1
6
Greatest
4, 6, 12
6, 9, 18
6
Common Factor
8.
9.
Greatest Common Factor
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
64: 1, 2,
4,
8
16, 32, 64
GFC = 16
10.
24: 1, 2, 3, 4,
6, 8, 12, 24
36: 1, 2, 3, 4,
6, 9, 12, 18, 36
42: 1, 2, 3,
6, 7, 14, 21, 42
GFC = 6
II.
1.
28 = 2 • 2• 7
21 = 3 • 7
GCF = 7
2.
84 = 2 • 2 • 3 • 7
72 = 2 • 2 • 2 • 3 • 3
GCF = 2 • 2 • 3 = 12
3.
4
18
9
GCF
=
=
=
=
2 • 2
2 • 3 • 3
3 • 3
1
26
39
52
GCF
=
=
=
=
2 • 13
3 • 13
2 • 2 • 13
13
4.
There is not a factor of 2 in 9.
There is not a factor of 3 in 4.
The only factor shared by all of
these numbers is 1.
5.
15 = 3 • 5
45 = 3 • 3 • 5
GCF = 15
When the smallest number is a factor of
the larger number, the smaller number
is their GCF.
REMEMBER 15 is a factor of 45; but 45
is a multiple of 15.
6.
30 = 2 • 3 • 5
49 = 7 • 7
GCF = 1
When there are no common prime factors,
the GCF is 1; because 1 is a factor of
every number.
BE SURE YOU DON'T CONFUSE GCF WITH LCM!
You will use GCF to simplify fractions.
Fraction answers must be given in simplified form.