a9b3 , a3b10

Since a9b3,a3b10 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 a9b3,a3b10:

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

2. Find the GCF for the variable part a9,b3,a3,b10

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:

a9,b3,a3,b10

The factors for a9 are a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a.

a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a

The factors for b3 are b⋅b⋅b.

b⋅b⋅b

The factors for a3 are a⋅a⋅a.

a⋅a⋅a

The factors for b10 are b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b.

b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b

List all the factors for a9,b3,a3,b10 to find the common factors.

a9=a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a

b3=b⋅b⋅b

a3=a⋅a⋅a

b10=b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b

The common factors for the variables a9,b3,a3,b10 are a⋅a⋅a⋅b⋅b⋅b.

a⋅a⋅a⋅b⋅b⋅b

The GCF for the variable part is a3b3.

GCFVariable=a3b3

Multiply the GCF of the numerical part 1 and the GCF of the variable part a3b3.

a3b3

Find the GCF a^9b^3 , a^3b^10