40n2m2 , 20m

Since 40n2m2,20m 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 40n2m2,20m:

1. Find the GCF for the numerical part 40,20

2. Find the GCF for the variable part n2,m2,m1

3. Multiply the values together

Find the common factors for the numerical part:

40,20

The factors for 40 are all numbers between 1 and 40, which divide 40 evenly.

Check numbers between 1 and 40

Find the factor pairs of 40 where x⋅y=40.

xy14022041058

List the factors for 40.

1,2,4,5,8,10,20,40

1,2,4,5,8,10,20,40

The factors for 20 are all numbers between 1 and 20, which divide 20 evenly.

Check numbers between 1 and 20

Find the factor pairs of 20 where x⋅y=20.

xy12021045

List the factors for 20.

1,2,4,5,10,20

1,2,4,5,10,20

List all the factors for 40,20 to find the common factors.

40: 1,2,4,5,8,10,20,40

20: 1,2,4,5,10,20

The common factors for 40,20 are 1,2,4,5,10,20.

1,2,4,5,10,20

The GCF for the numerical part is 20.

GCFNumerical=20

Next, find the common factors for the variable part:

n2,m2,m

The factors for n2 are n⋅n.

n⋅n

The factors for m2 are m⋅m.

m⋅m

The factor for m1 is m itself.

m

List all the factors for n2,m2,m1 to find the common factors.

n2=n⋅n

m2=m⋅m

m1=m

The common factor for the variables n2,m2,m1 is m.

m

The GCF for the variable part is m.

GCFVariable=m

Multiply the GCF of the numerical part 20 and the GCF of the variable part m.

20m

Find the GCF 40n^2m^2 , 20m