a2b2 , a3b

Since a2b2,a3b 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 a2b2,a3b:

1. Find the GCF for the numerical part 1,1

2. Find the GCF for the variable part a2,b2,a3,b1

3. Multiply the values together

Find the common factors for the numerical part:

1,1

The factors for 1 are all numbers between 1 and 1, which divide 1 evenly.

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

The factors for 1 are all numbers between 1 and 1, which divide 1 evenly.

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

List all the factors for 1,1 to find the common factors.

1: 1

1: 1

The common factors for 1,1 are 1.

1

The GCF for the numerical part is 1.

GCFNumerical=1

Next, find the common factors for the variable part:

a2,b2,a3,b

The factors for a2 are a⋅a.

a⋅a

The factors for b2 are b⋅b.

b⋅b

The factors for a3 are a⋅a⋅a.

a⋅a⋅a

The factor for b1 is b itself.

b

List all the factors for a2,b2,a3,b1 to find the common factors.

a2=a⋅a

b2=b⋅b

a3=a⋅a⋅a

b1=b

The common factors for the variables a2,b2,a3,b1 are a⋅a⋅b.

a⋅a⋅b

The GCF for the variable part is a2b.

GCFVariable=a2b

Multiply the GCF of the numerical part 1 and the GCF of the variable part a2b.

a2b

Find the GCF a^2b^2 , a^3b