Math 6High ( Period 3)

 Greatest Common Factor 2-2
A whole number that is a factor of two or more non zero whole numbers is a common factor of the two numbers.
Find all the common factors of 14 and 42
List all the factors of each number-- making a T chart of the factors as shown in class.
Factors of 14: 1, 2, 7, 14
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
You notice that the common factors as 1, 2, 7, and 14
The Greatest of these is 14
GCF(14, 42) = 14

Any two numbers have 1 as a common factor. the largest number that is a factor of two or more nonzero whole numbers is their greatest common factor ( GCF) or greatest common divisor (GCD)
Find the GCF of 28 and 36
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF( 28, 36) = 4

Find the GCF of 16 and 37
Factors of 16: 1, 2, 4, 8, 16
Factors of 37: 1, 37  (
GCF( 16, 37) = 1
If the GCF of 2 numbers is 1 the two numbers are said to be relatively prime. Notice the numbers do NOT need to be prime themselves. In this case, 37 is prime BUT 16 is not.

the GCF(8, 9)= 1
because
Factors of 8 : 1, 2, 4, 8
Factors of 9: 1, 3, 9
The only common factor they share is 1. 8 and 9 are said to be relatively prime-- even thought BOTH numbers are composite... neither is actually prime.

GCF ( 72, 84)
Making the T chart for these two numbers you discover that
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The greatest common factor is 12
We write
GCF(72, 84) = 12

What about GCF(66, 96)
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 18, 24, 32, 48, 96

WE discover that GCF(66, 96) = 6
The BOX method was shown in class. It is another way to discover what the GCF is for two numbers.
If you aren't sure, come in and I will review the BOX method for finding the GCF. You will want to know how to use it because we will use it to find the LCM as well-- later in this chapter.