The greatest common factor of two numbers is the largest number that divides both.
To find the greatest common factor of two numbers, say and , we start by listing the factors for each number.
Factors of :
Factors of :
The numbers and have two factors in common, and But we're looking for the greatest common factor, which is the largest of these factors.
Therefore, the greatest common factor of and is
What is the greatest common factor of and
Let's list the factors of each number. Then, we find the largest number that appears in both lists:
Factors of :
Factors of :
We conclude that the greatest common factor of and is
What is the greatest common factor of $2$ and $6?$
|
a
|
$12$ |
|
b
|
$1$ |
|
c
|
$2$ |
|
d
|
$6$ |
|
e
|
$3$ |
What is the greatest common factor of $6$ and $7?$
|
a
|
$1$ |
|
b
|
$6$ |
|
c
|
$2$ |
|
d
|
$7$ |
|
e
|
$3$ |
What is the greatest common factor of and
Let's list the factors of each number. Then, we find the largest number that appears in both lists:
Factors of :
Factors of :
We conclude that the greatest common factor of and is
What is the greatest common factor of $10$ and $22?$
|
a
|
$10$ |
|
b
|
$5$ |
|
c
|
$110$ |
|
d
|
$11$ |
|
e
|
$2$ |
What is the greatest common factor of $42$ and $98?$
|
a
|
$21$ |
|
b
|
$2$ |
|
c
|
$14$ |
|
d
|
$7$ |
|
e
|
$6$ |