a5b4 , a4b3

Since a5b4,a4b3 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 a5b4,a4b3:

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

2. Find the GCF for the variable part a5,b4,a4,b3

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:

a5,b4,a4,b3

The factors for a5 are a⋅a⋅a⋅a⋅a.

a⋅a⋅a⋅a⋅a

The factors for b4 are b⋅b⋅b⋅b.

b⋅b⋅b⋅b

The factors for a4 are a⋅a⋅a⋅a.

a⋅a⋅a⋅a

The factors for b3 are b⋅b⋅b.

b⋅b⋅b

List all the factors for a5,b4,a4,b3 to find the common factors.

a5=a⋅a⋅a⋅a⋅a

b4=b⋅b⋅b⋅b

a4=a⋅a⋅a⋅a

b3=b⋅b⋅b

The common factors for the variables a5,b4,a4,b3 are a⋅a⋅a⋅a⋅b⋅b⋅b.

a⋅a⋅a⋅a⋅b⋅b⋅b

The GCF for the variable part is a4b3.

GCFVariable=a4b3

Multiply the GCF of the numerical part 1 and the GCF of the variable part a4b3.

a4b3

Find the GCF a^5b^4 , a^4b^3