30×2 , 36×3 , 72×4

Since 30×2,36×3,72×4 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 30×2,36×3,72×4:

1. Find the GCF for the numerical part 30,36,72

2. Find the GCF for the variable part x2,x3,x4

3. Multiply the values together

Find the common factors for the numerical part:

30,36,72

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 36 are all numbers between 1 and 36, which divide 36 evenly.

Check numbers between 1 and 36

Find the factor pairs of 36 where x⋅y=36.

xy1362183124966

List the factors for 36.

1,2,3,4,6,9,12,18,36

1,2,3,4,6,9,12,18,36

The factors for 72 are all numbers between 1 and 72, which divide 72 evenly.

Check numbers between 1 and 72

Find the factor pairs of 72 where x⋅y=72.

xy17223632441861289

List the factors for 72.

1,2,3,4,6,8,9,12,18,24,36,72

1,2,3,4,6,8,9,12,18,24,36,72

List all the factors for 30,36,72 to find the common factors.

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

36: 1,2,3,4,6,9,12,18,36

72: 1,2,3,4,6,8,9,12,18,24,36,72

The common factors for 30,36,72 are 1,2,3,6.

1,2,3,6

The GCF for the numerical part is 6.

GCFNumerical=6

Next, find the common factors for the variable part:

x2,x3,x4

The factors for x2 are x⋅x.

x⋅x

The factors for x3 are x⋅x⋅x.

x⋅x⋅x

The factors for x4 are x⋅x⋅x⋅x.

x⋅x⋅x⋅x

List all the factors for x2,x3,x4 to find the common factors.

x2=x⋅x

x3=x⋅x⋅x

x4=x⋅x⋅x⋅x

The common factors for the variables x2,x3,x4 are x⋅x.

x⋅x

The GCF for the variable part is x2.

GCFVariable=x2

Multiply the GCF of the numerical part 6 and the GCF of the variable part x2.

6×2

Find the GCF 30x^2 , 36x^3 , 72x^4