21m2n5 , 35mn4

Since 21m2n5,35mn4 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 21m2n5,35mn4:

1. Find the GCF for the numerical part 21,35

2. Find the GCF for the variable part m2,n5,m1,n4

3. Multiply the values together

Find the common factors for the numerical part:

21,35

The factors for 21 are all numbers between 1 and 21, which divide 21 evenly.

Check numbers between 1 and 21

Find the factor pairs of 21 where x⋅y=21.

xy12137

List the factors for 21.

1,3,7,21

1,3,7,21

The factors for 35 are all numbers between 1 and 35, which divide 35 evenly.

Check numbers between 1 and 35

Find the factor pairs of 35 where x⋅y=35.

xy13557

List the factors for 35.

1,5,7,35

1,5,7,35

List all the factors for 21,35 to find the common factors.

21: 1,3,7,21

35: 1,5,7,35

The common factors for 21,35 are 1,7.

1,7

The GCF for the numerical part is 7.

GCFNumerical=7

Next, find the common factors for the variable part:

m2,n5,m,n4

The factors for m2 are m⋅m.

m⋅m

The factors for n5 are n⋅n⋅n⋅n⋅n.

n⋅n⋅n⋅n⋅n

The factor for m1 is m itself.

m

The factors for n4 are n⋅n⋅n⋅n.

n⋅n⋅n⋅n

List all the factors for m2,n5,m1,n4 to find the common factors.

m2=m⋅m

n5=n⋅n⋅n⋅n⋅n

m1=m

n4=n⋅n⋅n⋅n

The common factors for the variables m2,n5,m1,n4 are m⋅n⋅n⋅n⋅n.

m⋅n⋅n⋅n⋅n

The GCF for the variable part is mn4.

GCFVariable=mn4

Multiply the GCF of the numerical part 7 and the GCF of the variable part mn4.

7mn4

Find the GCF 21m^2n^5 , 35mn^4