# Find the GCF xy^3 , xy^2 , xy xy3 , xy2 , xy
Since xy3,xy2,xy contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.
Steps to find the GCF for xy3,xy2,xy:
1. Find the GCF for the numerical part 1,1,1
2. Find the GCF for the variable part x1,y3,x1,y2,x1,y1
3. Multiply the values together
Find the common factors for the numerical part:
1,1,1
The factors for 1 are 1.
The factors for 1 are all numbers between 1 and 1, which divide 1 evenly.
Check numbers between 1 and 1
Find the factor pairs of 1 where x⋅y=1.
xy11
List the factors for 1.
1
1
The factors for 1 are 1.
The factors for 1 are all numbers between 1 and 1, which divide 1 evenly.
Check numbers between 1 and 1
Find the factor pairs of 1 where x⋅y=1.
xy11
List the factors for 1.
1
1
The factors for 1 are 1.
The factors for 1 are all numbers between 1 and 1, which divide 1 evenly.
Check numbers between 1 and 1
Find the factor pairs of 1 where x⋅y=1.
xy11
List the factors for 1.
1
1
List all the factors for 1,1,1 to find the common factors.
1: 1
1: 1
1: 1
The common factors for 1,1,1 are 1.
1
The GCF for the numerical part is 1.
GCFNumerical=1
Next, find the common factors for the variable part:
x,y3,x,y2,x,y
The factor for x1 is x itself.
x
The factors for y3 are y⋅y⋅y.
y⋅y⋅y
The factor for x1 is x itself.
x
The factors for y2 are y⋅y.
y⋅y
The factor for x1 is x itself.
x
The factor for y1 is y itself.
y
List all the factors for x1,y3,x1,y2,x1,y1 to find the common factors.
x1=x
y3=y⋅y⋅y
x1=x
y2=y⋅y
x1=x
y1=y
The common factors for the variables x1,y3,x1,y2,x1,y1 are x⋅y.
x⋅y
The GCF for the variable part is xy.
GCFVariable=xy
Multiply the GCF of the numerical part 1 and the GCF of the variable part xy.
xy
Find the GCF xy^3 , xy^2 , xy     