17×3 , -35×4 , 7×5

Since 17×3,-35×4,7×5 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 17×3,-35×4,7×5:

1. Find the GCF for the numerical part 17,-35,7

2. Find the GCF for the variable part x3,x4,x5

3. Multiply the values together

Find the common factors for the numerical part:

17,-35,7

The factors for 17 are all numbers between 1 and 17, which divide 17 evenly.

Check numbers between 1 and 17

Find the factor pairs of 17 where x⋅y=17.

xy117

List the factors for 17.

1,17

1,17

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.

List the factors for -35.

-35,-7,-5,-1,1,5,7,35

-35,-7,-5,-1,1,5,7,35

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

List all the factors for 17,-35,7 to find the common factors.

17: 1,17

-35: -35,-7,-5,-1,1,5,7,35

7: 1,7

The common factors for 17,-35,7 are 1.

1

The GCF for the numerical part is 1.

GCFNumerical=1

Next, find the common factors for the variable part:

x3,x4,x5

The factors for x3 are x⋅x⋅x.

x⋅x⋅x

The factors for x4 are x⋅x⋅x⋅x.

x⋅x⋅x⋅x

The factors for x5 are x⋅x⋅x⋅x⋅x.

x⋅x⋅x⋅x⋅x

List all the factors for x3,x4,x5 to find the common factors.

x3=x⋅x⋅x

x4=x⋅x⋅x⋅x

x5=x⋅x⋅x⋅x⋅x

The common factors for the variables x3,x4,x5 are x⋅x⋅x.

x⋅x⋅x

The GCF for the variable part is x3.

GCFVariable=x3

Multiply the GCF of the numerical part 1 and the GCF of the variable part x3.

x3

Find the GCF 17x^3 , -35x^4 , 7x^5