x10y8 , x6y8 , x4y2

Since x10y8,x6y8,x4y2 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 x10y8,x6y8,x4y2:

1. Find the GCF for the numerical part 1,1,1

2. Find the GCF for the variable part x10,y8,x6,y8,x4,y2

3. Multiply the values together

Find the common factors for the numerical part:

1,1,1

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 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 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,y8,x6,y8,x4,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 y8 are y⋅y⋅y⋅y⋅y⋅y⋅y⋅y.

y⋅y⋅y⋅y⋅y⋅y⋅y⋅y

The factors for x6 are x⋅x⋅x⋅x⋅x⋅x.

x⋅x⋅x⋅x⋅x⋅x

The factors for y8 are y⋅y⋅y⋅y⋅y⋅y⋅y⋅y.

y⋅y⋅y⋅y⋅y⋅y⋅y⋅y

The factors for x4 are x⋅x⋅x⋅x.

x⋅x⋅x⋅x

The factors for y2 are y⋅y.

y⋅y

List all the factors for x10,y8,x6,y8,x4,y2 to find the common factors.

x10=x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x

y8=y⋅y⋅y⋅y⋅y⋅y⋅y⋅y

x6=x⋅x⋅x⋅x⋅x⋅x

y8=y⋅y⋅y⋅y⋅y⋅y⋅y⋅y

x4=x⋅x⋅x⋅x

y2=y⋅y

The common factors for the variables x10,y8,x6,y8,x4,y2 are x⋅x⋅x⋅x⋅y⋅y.

x⋅x⋅x⋅x⋅y⋅y

The GCF for the variable part is x4y2.

GCFVariable=x4y2

Multiply the GCF of the numerical part 1 and the GCF of the variable part x4y2.

x4y2

Find the GCF x^10y^8 , x^6y^8 , x^4y^2