mn3 , m4n , mn

Since mn3,m4n,mn 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 mn3,m4n,mn:

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

2. Find the GCF for the variable part m1,n3,m4,n1,m1,n1

3. Multiply the values together

Find the common factors for the numerical part:

1,1,1

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

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

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

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

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

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

List all the factors for 1,1,1 to find the common factors.

1: 1

1: 1

1: 1

The common factors for 1,1,1 are 1.

1

The GCF for the numerical part is 1.

GCFNumerical=1

Next, find the common factors for the variable part:

m,n3,m4,n,m,n

The factor for m1 is m itself.

m

The factors for n3 are n⋅n⋅n.

n⋅n⋅n

The factors for m4 are m⋅m⋅m⋅m.

m⋅m⋅m⋅m

The factor for n1 is n itself.

n

The factor for m1 is m itself.

m

The factor for n1 is n itself.

n

List all the factors for m1,n3,m4,n1,m1,n1 to find the common factors.

m1=m

n3=n⋅n⋅n

m4=m⋅m⋅m⋅m

n1=n

m1=m

n1=n

The common factors for the variables m1,n3,m4,n1,m1,n1 are m⋅n.

m⋅n

The GCF for the variable part is mn.

GCFVariable=mn

Multiply the GCF of the numerical part 1 and the GCF of the variable part mn.

mn

Find the GCF mn^3 , m^4n , mn