30×3 , 12×5 , 42×4

Since 30×3,12×5,42×4 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 30×3,12×5,42×4:

1. Find the GCF for the numerical part 30,12,42

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

3. Multiply the values together

Find the common factors for the numerical part:

30,12,42

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 12 are all numbers between 1 and 12, which divide 12 evenly.

Check numbers between 1 and 12

Find the factor pairs of 12 where x⋅y=12.

xy1122634

List the factors for 12.

1,2,3,4,6,12

1,2,3,4,6,12

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.

xy14222131467

List the factors for 42.

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

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

List all the factors for 30,12,42 to find the common factors.

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

12: 1,2,3,4,6,12

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

The common factors for 30,12,42 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:

x3,x5,x4

The factors for x3 are x⋅x⋅x.

x⋅x⋅x

The factors for x5 are x⋅x⋅x⋅x⋅x.

x⋅x⋅x⋅x⋅x

The factors for x4 are x⋅x⋅x⋅x.

x⋅x⋅x⋅x

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

x3=x⋅x⋅x

x5=x⋅x⋅x⋅x⋅x

x4=x⋅x⋅x⋅x

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

x⋅x⋅x

The GCF for the variable part is x3.

GCFVariable=x3

Multiply the GCF of the numerical part 6 and the GCF of the variable part x3.

6×3

Find the GCF 30x^3 , 12x^5 , 42x^4