15a3b , 40a2b2 , 15ab3

Since 15a3b,40a2b2,15ab3 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 15a3b,40a2b2,15ab3:

1. Find the GCF for the numerical part 15,40,15

2. Find the GCF for the variable part a3,b1,a2,b2,a1,b3

3. Multiply the values together

Find the common factors for the numerical part:

15,40,15

The factors for 15 are all numbers between 1 and 15, which divide 15 evenly.

Check numbers between 1 and 15

Find the factor pairs of 15 where x⋅y=15.

xy11535

List the factors for 15.

1,3,5,15

1,3,5,15

The factors for 40 are all numbers between 1 and 40, which divide 40 evenly.

Check numbers between 1 and 40

Find the factor pairs of 40 where x⋅y=40.

xy14022041058

List the factors for 40.

1,2,4,5,8,10,20,40

1,2,4,5,8,10,20,40

The factors for 15 are all numbers between 1 and 15, which divide 15 evenly.

Check numbers between 1 and 15

Find the factor pairs of 15 where x⋅y=15.

xy11535

List the factors for 15.

1,3,5,15

1,3,5,15

List all the factors for 15,40,15 to find the common factors.

15: 1,3,5,15

40: 1,2,4,5,8,10,20,40

15: 1,3,5,15

The common factors for 15,40,15 are 1,5.

1,5

The GCF for the numerical part is 5.

GCFNumerical=5

Next, find the common factors for the variable part:

a3,b,a2,b2,a,b3

The factors for a3 are a⋅a⋅a.

a⋅a⋅a

The factor for b1 is b itself.

b

The factors for a2 are a⋅a.

a⋅a

The factors for b2 are b⋅b.

b⋅b

The factor for a1 is a itself.

a

The factors for b3 are b⋅b⋅b.

b⋅b⋅b

List all the factors for a3,b1,a2,b2,a1,b3 to find the common factors.

a3=a⋅a⋅a

b1=b

a2=a⋅a

b2=b⋅b

a1=a

b3=b⋅b⋅b

The common factors for the variables a3,b1,a2,b2,a1,b3 are a⋅b.

a⋅b

The GCF for the variable part is ab.

GCFVariable=ab

Multiply the GCF of the numerical part 5 and the GCF of the variable part ab.

5ab

Find the GCF 15a^3b , 40a^2b^2 , 15ab^3