What is the gcf of 16x^5y^2+40x^4y^3

Step-by-step explanation:

Since  

16

x

5

y

2

,

40

x

4

y

3

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  

16

x

5

y

2

,

40

x

4

y

3

:

1. Find the GCF for the numerical part  

16

,

40

2. Find the GCF for the variable part  

x

5

,

y

2

,

x

4

,

y

3

3. Multiply the values together

Find the common factors for the numerical part:

16

,

40

The factors for  

16

are  

1

,

2

,

4

,

8

,

16

.

Tap for more steps...

1

,

2

,

4

,

8

,

16

The factors for  

40

are  

1

,

2

,

4

,

5

,

8

,

10

,

20

,

40

.

Tap for more steps...

1

,

2

,

4

,

5

,

8

,

10

,

20

,

40

List all the factors for  

16

,

40

to find the common factors.

16

:  

1

,

2

,

4

,

8

,

16

40

:  

1

,

2

,

4

,

5

,

8

,

10

,

20

,

40

The common factors for  

16

,

40

are  

1

,

2

,

4

,

8

.

1

,

2

,

4

,

8

The GCF for the numerical part is  

8

.

GCF

Numerical

=

8

Next, find the common factors for the variable part:

x

5

,

y

2

,

x

4

,

y

3

The factors for  

x

5

are  

x

⋅

x

⋅

x

⋅

x

⋅

x

.

x

⋅

x

⋅

x

⋅

x

⋅

x

The factors for  

y

2

are  

y

⋅

y

.

y

⋅

y

The factors for  

x

4

are  

x

⋅

x

⋅

x

⋅

x

.

x

⋅

x

⋅

x

⋅

x

The factors for  

y

3

are  

y

⋅

y

⋅

y

.

y

⋅

y

⋅

y

List all the factors for  

x

5

,

y

2

,

x

4

,

y

3

to find the common factors.

x

5

=

x

⋅

x

⋅

x

⋅

x

⋅

x

y

2

=

y

⋅

y

x

4

=

x

⋅

x

⋅

x

⋅

x

y

3

=

y

⋅

y

⋅

y

The common factors for the variables  

x

5

,

y

2

,

x

4

,

y

3

are  

x

⋅

x

⋅

x

⋅

x

⋅

y

⋅

y

.

x

⋅

x

⋅

x

⋅

x

⋅

y

⋅

y

The GCF for the variable part is  

x

4

y

2

.

GCF

Variable

=

x

4

y

2

Multiply the GCF of the numerical part  

8

and the GCF of the variable part  

x

4

y

2

.

8

x

4

y

2