Find the GCF 42p^6q^3-70p^5qr^2

Since ${\displaystyle 42p^6{q}^3,-70p^{5}q{r}^2}$ 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 ${\displaystyle 42p^6{q}^3,-70p^{5}q{r}^2}$:

1. Find the GCF for the numerical part ${\displaystyle 42,-70}$

2. Find the GCF for the variable part ${\displaystyle p^6,q^3,p^5,q^1,r^2}$

3. Multiply the values together

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 42,-70}$ to find the common factors.

${\displaystyle 42}$: ${\displaystyle 1,2,3,6,7,14,21,42}$

${\displaystyle -70}$: ${\displaystyle -70,-35,-14,-10,-7,-5,-2,-1,1,2,5,7,10,14,35,70}$

The common factors for ${\displaystyle 42,-70}$ are ${\displaystyle 1,2,7,14}$.

The GCF for the numerical part is ${\displaystyle 14}$.

Next, find the common factors for the variable part:

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

The factors for ${\displaystyle q^3}$ are ${\displaystyle q\cdot q\cdot q}$.

The factors for ${\displaystyle p^5}$ are ${\displaystyle p\cdot p\cdot p\cdot p\cdot p}$.

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

q

The factors for ${\displaystyle r^2}$ are ${\displaystyle r\cdot r}$.

List all the factors for ${\displaystyle p^6,q^3,p^5,q^1,r^2}$ to find the common factors.

The common factors for the variables ${\displaystyle p^6,q^3,p^5,q^1,r^2}$ are ${\displaystyle p\cdot p\cdot p\cdot p\cdot p\cdot q}$.

The GCF for the variable part is ${\displaystyle p^{5}q}$.