30y3 , 20y2

Since 30y3,20y2 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 30y3,20y2:

1. Find the GCF for the numerical part 30,20

2. Find the GCF for the variable part y3,y2

3. Multiply the values together

Find the common factors for the numerical part:

30,20

The factors for 30 are all numbers between 1 and 30, which divide 30 evenly.

Check numbers between 1 and 30

Find the factor pairs of 30 where x⋅y=30.

xy13021531056

List the factors for 30.

1,2,3,5,6,10,15,30

1,2,3,5,6,10,15,30

The factors for 20 are all numbers between 1 and 20, which divide 20 evenly.

Check numbers between 1 and 20

Find the factor pairs of 20 where x⋅y=20.

xy12021045

List the factors for 20.

1,2,4,5,10,20

1,2,4,5,10,20

List all the factors for 30,20 to find the common factors.

30: 1,2,3,5,6,10,15,30

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

The common factors for 30,20 are 1,2,5,10.

1,2,5,10

The GCF for the numerical part is 10.

GCFNumerical=10

Next, find the common factors for the variable part:

y3,y2

The factors for y3 are y⋅y⋅y.

y⋅y⋅y

The factors for y2 are y⋅y.

y⋅y

List all the factors for y3,y2 to find the common factors.

y3=y⋅y⋅y

y2=y⋅y

The common factors for the variables y3,y2 are y⋅y.

y⋅y

The GCF for the variable part is y2.

GCFVariable=y2

Multiply the GCF of the numerical part 10 and the GCF of the variable part y2.

10y2

Find the GCF 30y^3 , 20y^2