18xy , 36 , 54xy

Since 18xy,36,54xy 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 18xy,36,54xy:

1. Find the GCF for the numerical part 18,36,54

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

3. Multiply the values together

Find the common factors for the numerical part:

18,36,54

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 36 are all numbers between 1 and 36, which divide 36 evenly.

Check numbers between 1 and 36

Find the factor pairs of 36 where x⋅y=36.

xy1362183124966

List the factors for 36.

1,2,3,4,6,9,12,18,36

1,2,3,4,6,9,12,18,36

The factors for 54 are all numbers between 1 and 54, which divide 54 evenly.

Check numbers between 1 and 54

Find the factor pairs of 54 where x⋅y=54.

xy15422731869

List the factors for 54.

1,2,3,6,9,18,27,54

1,2,3,6,9,18,27,54

List all the factors for 18,36,54 to find the common factors.

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

36: 1,2,3,4,6,9,12,18,36

54: 1,2,3,6,9,18,27,54

The common factors for 18,36,54 are 1,2,3,6,9,18.

1,2,3,6,9,18

The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors 1,2,3,6,9,18 is 18.

18

Find the GCF 18xy , 36 , 54xy