Find the GCF 21m^5n^2+6m^3n+15m^2

Since ${\displaystyle 21m^5{n}^2,6m^{3}n,15m^2}$ 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 ${\displaystyle 21m^5{n}^2,6m^{3}n,15m^2}$:

1. Find the GCF for the numerical part ${\displaystyle 21,6,15}$

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

3. Multiply the values together

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 21,6,15}$ to find the common factors.

${\displaystyle 21}$: ${\displaystyle 1,3,7,21}$

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

${\displaystyle 15}$: ${\displaystyle 1,3,5,15}$

The common factors for ${\displaystyle 21,6,15}$ 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 ${\displaystyle m^3}$ are ${\displaystyle m\cdot m\cdot m}$.

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

n

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

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

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

The GCF for the variable part is ${\displaystyle m^2}$.