Math 6H ( Periods 3, 6, & 7)

Greatest Common Factor 5-5

Also check out December 1, 2009 posting of GCF. Here is a review of that lesson...


When the factors in the numbers 30 and 42 are listed, the numbers 1, 2, 3, and 6 appear in both lists
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

These numbers are called common factors of 30 and 42. The number 6 is the greatest of these numbers and is therefore called the greatest common factor of the two numbers.
We write
GCF(30,42) = 6
to denote the greatest common factor of 30 and 42

Find GCF(54, 72)
List the factors of each number

54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

the common factors are 1, 2, 3, 6, 9, and 18

the greatest number in both lists is 18. Therefore,

GCF(54, 72) = 18

Another way to find the GCF of two numbers is to use prime factorization.
Find GCF (54, 72)
First find the prime factorization of 54 and of 75

54 = 2∙3∙3∙3∙3
72 = 2∙2∙2∙3∙3

Find the greatest power of 2 that occurs in both prime factorization. 2
Find the greatest power of 3 that occurs in both prime factorization 3²
Therefore GCF(54,72) = 2∙3² = 18

Try GCF(45, 60) using the prime factorization method

The number 1 is a common factor of any two whole numbers.
If 1 is the GCF, then the two numbers are said to be relatively prime.
Show that 15 and 16 are relatively prime
List the factors of each number
Factors of 15 = 1, 3, 5, 15
Factors of 16: 1, 2, 4, 8, 16
Since the GCF(15, 16) = 1, the two numbers are relatively prime