30xy2 , 60xy , 90

Since 30xy2,60xy,90 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 30xy2,60xy,90:

1. Find the GCF for the numerical part 30,60,90

2. Find the GCF for the variable part x1,y2,x1,y1

3. Multiply the values together

Find the common factors for the numerical part:

30,60,90

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 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

The factors for 90 are all numbers between 1 and 90, which divide 90 evenly.

Check numbers between 1 and 90

Find the factor pairs of 90 where x⋅y=90.

xy190245330518615910

List the factors for 90.

1,2,3,5,6,9,10,15,18,30,45,90

1,2,3,5,6,9,10,15,18,30,45,90

List all the factors for 30,60,90 to find the common factors.

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

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

90: 1,2,3,5,6,9,10,15,18,30,45,90

The common factors for 30,60,90 are 1,2,3,5,6,10,15,30.

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

The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors 1,2,3,5,6,10,15,30 is 30.

30

Find the GCF 30xy^2 , 60xy , 90