7xy2 , 49×2 , 35x2y2

Since 7xy2,49×2,35x2y2 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 7xy2,49×2,35x2y2:

1. Find the GCF for the numerical part 7,49,35

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

3. Multiply the values together

Find the common factors for the numerical part:

7,49,35

The factors for 7 are all numbers between 1 and 7, which divide 7 evenly.

Check numbers between 1 and 7

Find the factor pairs of 7 where x⋅y=7.

xy17

List the factors for 7.

1,7

1,7

The factors for 49 are all numbers between 1 and 49, which divide 49 evenly.

Check numbers between 1 and 49

Find the factor pairs of 49 where x⋅y=49.

xy14977

List the factors for 49.

1,7,49

1,7,49

The factors for 35 are all numbers between 1 and 35, which divide 35 evenly.

Check numbers between 1 and 35

Find the factor pairs of 35 where x⋅y=35.

xy13557

List the factors for 35.

1,5,7,35

1,5,7,35

List all the factors for 7,49,35 to find the common factors.

7: 1,7

49: 1,7,49

35: 1,5,7,35

The common factors for 7,49,35 are 1,7.

1,7

The GCF for the numerical part is 7.

GCFNumerical=7

Next, find the common factors for the variable part:

x,y2,x2,x2,y2

The factor for x1 is x itself.

x

The factors for y2 are y⋅y.

y⋅y

The factors for x2 are x⋅x.

x⋅x

The factors for y2 are y⋅y.

y⋅y

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

x1=x

y2=y⋅y

x2=x⋅x

x2=x⋅x

y2=y⋅y

The common factor for the variables x1,y2,x2,x2,y2 is x.

x

The GCF for the variable part is x.

GCFVariable=x

Multiply the GCF of the numerical part 7 and the GCF of the variable part x.

7x

Find the GCF 7xy^2 , 49x^2 , 35x^2y^2