Find the GCF 12ab^3+20b

Since ${\displaystyle 12a{b}^3,20b}$ 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 ${\displaystyle 12a{b}^3,20b}$:

1. Find the GCF for the numerical part ${\displaystyle 12,20}$

2. Find the GCF for the variable part ${\displaystyle a^1,b^3,b^1}$

3. Multiply the values together

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 12,20}$ to find the common factors.

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

${\displaystyle 20}$: ${\displaystyle 1,2,4,5,10,20}$

The common factors for ${\displaystyle 12,20}$ are ${\displaystyle 1,2,4}$.

The GCF for the numerical part is ${\displaystyle 4}$.

Next, find the common factors for the variable part:

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

a

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

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

b

List all the factors for ${\displaystyle a^1,b^3,b^1}$ to find the common factors.

The common factor for the variables ${\displaystyle a^1,b^3,b^1}$ is ${\displaystyle b}$.

b

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