18x , 20xy

Since 18x,20xy 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 18x,20xy:

1. Find the GCF for the numerical part 18,20

2. Find the GCF for the variable part x1,x1,y1

3. Multiply the values together

Find the common factors for the numerical part:

18,20

The factors for 18 are all numbers between 1 and 18, which divide 18 evenly.

Check numbers between 1 and 18

Find the factor pairs of 18 where x⋅y=18.

xy1182936

List the factors for 18.

1,2,3,6,9,18

1,2,3,6,9,18

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 18,20 to find the common factors.

18: 1,2,3,6,9,18

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

The common factors for 18,20 are 1,2.

1,2

The GCF for the numerical part is 2.

GCFNumerical=2

Next, find the common factors for the variable part:

x,x,y

The factor for x1 is x itself.

x

The factor for y1 is y itself.

y

List all the factors for x1,x1,y1 to find the common factors.

x1=x

x1=x

y1=y

The common factor for the variables x1,x1,y1 is x.

x

The GCF for the variable part is x.

GCFVariable=x

Multiply the GCF of the numerical part 2 and the GCF of the variable part x.

2x

Find the GCF 18x , 20xy