40w5 , w2 , 14w4 , w7

Since 40w5,w2,14w4,w7 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 40w5,w2,14w4,w7:

1. Find the GCF for the numerical part 40,1,14,1

2. Find the GCF for the variable part w5,w2,w4,w7

3. Multiply the values together

Find the common factors for the numerical part:

40,1,14,1

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 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 14 are all numbers between 1 and 14, which divide 14 evenly.

Check numbers between 1 and 14

Find the factor pairs of 14 where x⋅y=14.

xy11427

List the factors for 14.

1,2,7,14

1,2,7,14

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 40,1,14,1 to find the common factors.

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

1: 1

14: 1,2,7,14

1: 1

The common factors for 40,1,14,1 are 1.

1

The GCF for the numerical part is 1.

GCFNumerical=1

Next, find the common factors for the variable part:

w5,w2,w4,w7

The factors for w5 are w⋅w⋅w⋅w⋅w.

w⋅w⋅w⋅w⋅w

The factors for w2 are w⋅w.

w⋅w

The factors for w4 are w⋅w⋅w⋅w.

w⋅w⋅w⋅w

The factors for w7 are w⋅w⋅w⋅w⋅w⋅w⋅w.

w⋅w⋅w⋅w⋅w⋅w⋅w

List all the factors for w5,w2,w4,w7 to find the common factors.

w5=w⋅w⋅w⋅w⋅w

w2=w⋅w

w4=w⋅w⋅w⋅w

w7=w⋅w⋅w⋅w⋅w⋅w⋅w

The common factors for the variables w5,w2,w4,w7 are w⋅w.

w⋅w

The GCF for the variable part is w2.

GCFVariable=w2

Multiply the GCF of the numerical part 1 and the GCF of the variable part w2.

w2

Find the GCF 40w^5 , w^2 , 14w^4 , w^7