-21×2 , 35×3

Since -21×2,35×3 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 -21×2,35×3:

1. Find the GCF for the numerical part -21,35

2. Find the GCF for the variable part x2,x3

3. Multiply the values together

Find the common factors for the numerical part:

-21,35

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.

List the factors for -21.

-21,-7,-3,-1,1,3,7,21

-21,-7,-3,-1,1,3,7,21

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 -21,35 to find the common factors.

-21: -21,-7,-3,-1,1,3,7,21

35: 1,5,7,35

The common factors for -21,35 are 1,7.

1,7

The GCF for the numerical part is 7.

GCFNumerical=7

Next, find the common factors for the variable part:

x2,x3

The factors for x2 are x⋅x.

x⋅x

The factors for x3 are x⋅x⋅x.

x⋅x⋅x

List all the factors for x2,x3 to find the common factors.

x2=x⋅x

x3=x⋅x⋅x

The common factors for the variables x2,x3 are x⋅x.

x⋅x

The GCF for the variable part is x2.

GCFVariable=x2

Multiply the GCF of the numerical part 7 and the GCF of the variable part x2.

7×2

Find the GCF -21x^2 , 35x^3