72xy , 36x2y , 84xy2

Since 72xy,36x2y,84xy2 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 72xy,36x2y,84xy2:

1. Find the GCF for the numerical part 72,36,84

2. Find the GCF for the variable part x1,y1,x2,y1,x1,y2

3. Multiply the values together

Find the common factors for the numerical part:

72,36,84

The factors for 72 are all numbers between 1 and 72, which divide 72 evenly.

Check numbers between 1 and 72

Find the factor pairs of 72 where x⋅y=72.

xy17223632441861289

List the factors for 72.

1,2,3,4,6,8,9,12,18,24,36,72

1,2,3,4,6,8,9,12,18,24,36,72

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 84 are all numbers between 1 and 84, which divide 84 evenly.

Check numbers between 1 and 84

Find the factor pairs of 84 where x⋅y=84.

xy184242328421614712

List the factors for 84.

1,2,3,4,6,7,12,14,21,28,42,84

1,2,3,4,6,7,12,14,21,28,42,84

List all the factors for 72,36,84 to find the common factors.

72: 1,2,3,4,6,8,9,12,18,24,36,72

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

84: 1,2,3,4,6,7,12,14,21,28,42,84

The common factors for 72,36,84 are 1,2,3,4,6,12.

1,2,3,4,6,12

The GCF for the numerical part is 12.

GCFNumerical=12

Next, find the common factors for the variable part:

x,y,x2,y,x,y2

The factor for x1 is x itself.

x

The factor for y1 is y itself.

y

The factors for x2 are x⋅x.

x⋅x

The factor for y1 is y itself.

y

The factor for x1 is x itself.

x

The factors for y2 are y⋅y.

y⋅y

List all the factors for x1,y1,x2,y1,x1,y2 to find the common factors.

x1=x

y1=y

x2=x⋅x

y1=y

x1=x

y2=y⋅y

The common factors for the variables x1,y1,x2,y1,x1,y2 are x⋅y.

x⋅y

The GCF for the variable part is xy.

GCFVariable=xy

Multiply the GCF of the numerical part 12 and the GCF of the variable part xy.

12xy

Find the GCF 72xy , 36x^2y , 84xy^2