1: The Greatest Common Factor (GCF) is the largest number that will divide into the other factors, in the expression. This means there are no larger factors, or numbers, that can divide into the factors of the expression.  x2+14x+21 would have a GCF of 7. There is no other number that will go into 14 and 21. The GCF must be able to divide into both factors. x2+36x+60 would have a GCF of 12. We must be careful when determining the GCF to ensure that we have attempted every number possible as to not miss the GCF.

If the expression is prime, is the entire expression written as the GCF?

2:The greatest common factor (GCF) of two or more whole numbers is the largest whole number that divides evenly into each of the numbers. The way that I like to find the GCF is by listing or thinking of all the factors of each number. Then, I list the common factors and pick the largest one. For example,

• 9 and 12

Factors: 9:1,3,9

12:1,2,3,4,6,12

GCF: 3                                 Simplified fraction 9/12= 3/4

Being that the GCF is the product of the factors that these numbers have in common, you know that it is a factor of both numbers.

3:The Greatest Common Factor (GCF) is the largest number that will divide into the other factors, in the expression. This means there are no larger factors, or numbers, that can divide into the factors of the expression.  x2+14x+21 would have a GCF of 7. There is no other number that will go into 14 and 21. The GCF must be able to divide into both factors. x2+36x+60 would have a GCF of 12. We must be careful when determining the GCF to ensure that we have attempted every number possible as to not miss the GCF.

If the expression is prime, is the entire expression written as the GCF?