40n3m , 4m2n2

Since 40n3m,4m2n2 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 40n3m,4m2n2:

1. Find the GCF for the numerical part 40,4

2. Find the GCF for the variable part n3,m1,m2,n2

3. Multiply the values together

Find the common factors for the numerical part:

40,4

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 4 are all numbers between 1 and 4, which divide 4 evenly.

Check numbers between 1 and 4

Find the factor pairs of 4 where x⋅y=4.

xy1422

List the factors for 4.

1,2,4

1,2,4

List all the factors for 40,4 to find the common factors.

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

4: 1,2,4

The common factors for 40,4 are 1,2,4.

1,2,4

The GCF for the numerical part is 4.

GCFNumerical=4

Next, find the common factors for the variable part:

n3,m,m2,n2

The factors for n3 are n⋅n⋅n.

n⋅n⋅n

The factor for m1 is m itself.

m

The factors for m2 are m⋅m.

m⋅m

The factors for n2 are n⋅n.

n⋅n

List all the factors for n3,m1,m2,n2 to find the common factors.

n3=n⋅n⋅n

m1=m

m2=m⋅m

n2=n⋅n

The common factors for the variables n3,m1,m2,n2 are n⋅n⋅m.

n⋅n⋅m

The GCF for the variable part is mn2.

GCFVariable=mn2

Multiply the GCF of the numerical part 4 and the GCF of the variable part mn2.

4mn2

Find the GCF 40n^3m , 4m^2n^2