Find the GCF x^10y^4 , x^8y^2 , x^9y^2

x10y4 , x8y2 , x9y2
Since x10y4,x8y2,x9y2 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 x10y4,x8y2,x9y2:
1. Find the GCF for the numerical part 1,1,1
2. Find the GCF for the variable part x10,y4,x8,y2,x9,y2
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:
x10,y4,x8,y2,x9,y2
The factors for x10 are x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x.
x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
The factors for y4 are y⋅y⋅y⋅y.
y⋅y⋅y⋅y
The factors for x8 are x⋅x⋅x⋅x⋅x⋅x⋅x⋅x.
x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
The factors for y2 are y⋅y.
y⋅y
The factors for x9 are x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x.
x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
The factors for y2 are y⋅y.
y⋅y
List all the factors for x10,y4,x8,y2,x9,y2 to find the common factors.
x10=x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
y4=y⋅y⋅y⋅y
x8=x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
y2=y⋅y
x9=x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
y2=y⋅y
The common factors for the variables x10,y4,x8,y2,x9,y2 are x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅y⋅y.
x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅y⋅y
The GCF for the variable part is x8y2.
GCFVariable=x8y2
Multiply the GCF of the numerical part 1 and the GCF of the variable part x8y2.
x8y2
Find the GCF x^10y^4 , x^8y^2 , x^9y^2