Find the GCF 12m^5n^2-6m^2n^3+3mn

Since ${\displaystyle 12m^5{n}^2,-6m^2{n}^3,3mn}$ 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 ${\displaystyle 12m^5{n}^2,-6m^2{n}^3,3mn}$:

1. Find the GCF for the numerical part ${\displaystyle 12,-6,3}$

2. Find the GCF for the variable part ${\displaystyle m^5,n^2,m^2,n^3,m^1,n^1}$

3. Multiply the values together

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 12,-6,3}$ to find the common factors.

${\displaystyle 12}$: ${\displaystyle 1,2,3,4,6,12}$

${\displaystyle -6}$: ${\displaystyle -6,-3,-2,-1,1,2,3,6}$

${\displaystyle 3}$: ${\displaystyle 1,3}$

The common factors for ${\displaystyle 12,-6,3}$ are ${\displaystyle 1,3}$.

The GCF for the numerical part is ${\displaystyle 3}$.

Next, find the common factors for the variable part:

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

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

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

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

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

m

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

n

List all the factors for ${\displaystyle m^5,n^2,m^2,n^3,m^1,n^1}$ to find the common factors.

The common factors for the variables ${\displaystyle m^5,n^2,m^2,n^3,m^1,n^1}$ are ${\displaystyle m\cdot n}$.

The GCF for the variable part is ${\displaystyle mn}$.