Find the GCF 792x^9y^13z^4

The GCF of a single polynomial is itself.

Since ${\displaystyle 792x^9{y}^{13}{z}^4}$ 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.

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 792}$ to find the common factors.

The common factors for ${\displaystyle 792}$ are ${\displaystyle 1,2,3,4,6,8,9,11,12,18,22,24,33,36,44,66,72,88,99,132,198,264,396,792}$.

The GCF for the numerical part is ${\displaystyle 792}$.

Next, find the common factors for the variable part:

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 ${\displaystyle y^{13}}$ are ${\displaystyle y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}$.

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

List all the factors for ${\displaystyle x^9,y^{13},z^4}$ to find the common factors.

The common factors for the variables ${\displaystyle x^9,y^{13},z^4}$ are ${\displaystyle x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot z\cdot z\cdot z\cdot z}$.

The GCF for the variable part is ${\displaystyle x^9{y}^{13}{z}^4}$.