18k , 15k3

Since 18k,15k3 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 18k,15k3:

1. Find the GCF for the numerical part 18,15

2. Find the GCF for the variable part k1,k3

3. Multiply the values together

Find the common factors for the numerical part:

18,15

The factors for 18 are all numbers between 1 and 18, which divide 18 evenly.

Check numbers between 1 and 18

Find the factor pairs of 18 where x⋅y=18.

xy1182936

List the factors for 18.

1,2,3,6,9,18

1,2,3,6,9,18

The factors for 15 are all numbers between 1 and 15, which divide 15 evenly.

Check numbers between 1 and 15

Find the factor pairs of 15 where x⋅y=15.

xy11535

List the factors for 15.

1,3,5,15

1,3,5,15

List all the factors for 18,15 to find the common factors.

18: 1,2,3,6,9,18

15: 1,3,5,15

The common factors for 18,15 are 1,3.

1,3

The GCF for the numerical part is 3.

GCFNumerical=3

Next, find the common factors for the variable part:

k,k3

The factor for k1 is k itself.

k

The factors for k3 are k⋅k⋅k.

k⋅k⋅k

List all the factors for k1,k3 to find the common factors.

k1=k

k3=k⋅k⋅k

The common factor for the variables k1,k3 is k.

k

The GCF for the variable part is k.

GCFVariable=k

Multiply the GCF of the numerical part 3 and the GCF of the variable part k.

3k

Find the GCF 18k , 15k^3