-42x2y , 21x2y2 , 84x2y4

Since -42x2y,21x2y2,84x2y4 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 -42x2y,21x2y2,84x2y4:

1. Find the GCF for the numerical part -42,21,84

2. Find the GCF for the variable part x2,y1,x2,y2,x2,y4

3. Multiply the values together

Find the common factors for the numerical part:

-42,21,84

The factors for -42 are all numbers between 1 and 42, which divide -42 evenly.

Check numbers between 1 and 42

Find the factor pairs of -42 where x⋅y=-42.

List the factors for -42.

-42,-21,-14,-7,-6,-3,-2,-1,1,2,3,6,7,14,21,42

-42,-21,-14,-7,-6,-3,-2,-1,1,2,3,6,7,14,21,42

The factors for 21 are all numbers between 1 and 21, which divide 21 evenly.

Check numbers between 1 and 21

Find the factor pairs of 21 where x⋅y=21.

xy12137

List the factors for 21.

1,3,7,21

1,3,7,21

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 -42,21,84 to find the common factors.

-42: -42,-21,-14,-7,-6,-3,-2,-1,1,2,3,6,7,14,21,42

21: 1,3,7,21

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

The common factors for -42,21,84 are 1,3,7,21.

1,3,7,21

The GCF for the numerical part is 21.

GCFNumerical=21

Next, find the common factors for the variable part:

x2,y,x2,y2,x2,y4

The factors for x2 are x⋅x.

x⋅x

The factor for y1 is y itself.

y

The factors for x2 are x⋅x.

x⋅x

The factors for y2 are y⋅y.

y⋅y

The factors for x2 are x⋅x.

x⋅x

The factors for y4 are y⋅y⋅y⋅y.

y⋅y⋅y⋅y

List all the factors for x2,y1,x2,y2,x2,y4 to find the common factors.

x2=x⋅x

y1=y

x2=x⋅x

y2=y⋅y

x2=x⋅x

y4=y⋅y⋅y⋅y

The common factors for the variables x2,y1,x2,y2,x2,y4 are x⋅x⋅y.

x⋅x⋅y

The GCF for the variable part is x2y.

GCFVariable=x2y

Multiply the GCF of the numerical part 21 and the GCF of the variable part x2y.

21x2y

Find the GCF -42x^2y , 21x^2y^2 , 84x^2y^4