Monday, October 23, 2006
What Is The Greatest Common Factor (GCF) Of 60 And 72?
We are trying to find the largest (or greatest) number that is a factor of both 60 and 72.
You could use either of the following methods to find the greatest common factor.
Method 1.
List all of the factors of each number.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
1, 2, 3, 4, 6 and 12 are the factors common to both 60 and 72. The largest (greatest) of these is 12. Therefore, 12 is the greatest common factor of 60 and 72.
Method 2.
Write each number as a product of its prime factors.
60 = 2 x 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
Find those prime factors are common to both 60 and 72.
60 = 2 x 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
Now, multiply the prime factors are common to both 60 and 72 to find the GCF.
2 x 2 x 3 = 12
12 is the greatest common factor of 60 and 72.
12 is the greatest common factor of 60 and 72.
