30×3 , 110×4 , 60×5

Since 30×3,110×4,60×5 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 30×3,110×4,60×5:

1. Find the GCF for the numerical part 30,110,60

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

3. Multiply the values together

Find the common factors for the numerical part:

30,110,60

The factors for 30 are all numbers between 1 and 30, which divide 30 evenly.

Check numbers between 1 and 30

Find the factor pairs of 30 where x⋅y=30.

xy13021531056

List the factors for 30.

1,2,3,5,6,10,15,30

1,2,3,5,6,10,15,30

The factors for 110 are all numbers between 1 and 110, which divide 110 evenly.

Check numbers between 1 and 110

Find the factor pairs of 110 where x⋅y=110.

xy11102555221011

List the factors for 110.

1,2,5,10,11,22,55,110

1,2,5,10,11,22,55,110

The factors for 60 are all numbers between 1 and 60, which divide 60 evenly.

Check numbers between 1 and 60

Find the factor pairs of 60 where x⋅y=60.

xy160230320415512610

List the factors for 60.

1,2,3,4,5,6,10,12,15,20,30,60

1,2,3,4,5,6,10,12,15,20,30,60

List all the factors for 30,110,60 to find the common factors.

30: 1,2,3,5,6,10,15,30

110: 1,2,5,10,11,22,55,110

60: 1,2,3,4,5,6,10,12,15,20,30,60

The common factors for 30,110,60 are 1,2,5,10.

1,2,5,10

The GCF for the numerical part is 10.

GCFNumerical=10

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 10 and the GCF of the variable part x3.

10×3

Find the GCF 30x^3 , 110x^4 , 60x^5