Find the GCF x^10y^10 , x^9y^9 , xy^10 , x^4y^6

Since ${\displaystyle x^{10}{y}^{10},x^9{y}^9,x{y}^{10},x^4{y}^6}$ contains 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.

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 1,1,1,1}$ to find the common factors.

The common factors for ${\displaystyle 1,1,1,1}$ are ${\displaystyle 1}$.

The GCF for the numerical part is ${\displaystyle 1}$.

Next, find the common factors for the variable part:

The factors for ${\displaystyle x^{10}}$ are ${\displaystyle x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}$.

The factors for ${\displaystyle y^{10}}$ are ${\displaystyle y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}$.

The factors for ${\displaystyle x^9}$ are ${\displaystyle x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}$.

The factors for ${\displaystyle y^9}$ are ${\displaystyle y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}$.

The factor for ${\displaystyle x^1}$ is ${\displaystyle x}$ itself.

The factors for ${\displaystyle y^{10}}$ are ${\displaystyle y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}$.

The factors for ${\displaystyle x^4}$ are ${\displaystyle x\cdot x\cdot x\cdot x}$.

The factors for ${\displaystyle y^6}$ are ${\displaystyle y\cdot y\cdot y\cdot y\cdot y\cdot y}$.

List all the factors for ${\displaystyle x^{10},y^{10},x^9,y^9,x^1,y^{10},x^4,y^6}$ to find the common factors.

The common factors for the variables ${\displaystyle x^{10},y^{10},x^9,y^9,x^1,y^{10},x^4,y^6}$ are ${\displaystyle x\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}$.

The GCF for the variable part is ${\displaystyle x{y}^6}$.