Find the GCF 8ab-56a

Since ${\displaystyle 8ab,-56a}$ 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 ${\displaystyle 8ab,-56a}$:

1. Find the GCF for the numerical part ${\displaystyle 8,-56}$

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

3. Multiply the values together

Find the common factors for the numerical part:

List all the factors for ${\displaystyle 8,-56}$ to find the common factors.

${\displaystyle 8}$: ${\displaystyle 1,2,4,8}$

${\displaystyle -56}$: ${\displaystyle -56,-28,-14,-8,-7,-4,-2,-1,1,2,4,7,8,14,28,56}$

The common factors for ${\displaystyle 8,-56}$ are ${\displaystyle 1,2,4,8}$.

The GCF for the numerical part is ${\displaystyle 8}$.

Next, find the common factors for the variable part:

a,b,a

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

a

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

b

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

a

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

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

a

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