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## Find the greatest common factor. 3x^2a+3xa^2

Question

Find the greatest common factor.

3x^2a+3xa^2

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Mathematics
3 years
2021-08-30T02:00:34+00:00
2021-08-30T02:00:34+00:00 2 Answers
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## Answers ( )

Since

3

x

2

a

,

3

x

a

2

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

3

x

2

a

,

3

x

a

2

:

1. Find the GCF for the numerical part

3

,

3

2. Find the GCF for the variable part

x

2

,

a

1

,

x

1

,

a

2

3. Multiply the values together

Find the common factors for the numerical part:

3

,

3

The factors for

3

are

1

,

3

.

Tap for more steps…

1

,

3

The factors for

3

are

1

,

3

.

Tap for more steps…

1

,

3

List all the factors for

3

,

3

to find the common factors.

3

:

1

,

3

3

:

1

,

3

The common factors for

3

,

3

are

1

,

3

.

1

,

3

The GCF for the numerical part is

3

.

GCF

Numerical

=

3

Next, find the common factors for the variable part:

x

2

,

a

,

x

,

a

2

The factors for

x

2

are

x

⋅

x

.

x

⋅

x

The factor for

a

1

is

a

itself.

a

The factor for

x

1

is

x

itself.

x

The factors for

a

2

are

a

⋅

a

.

a

⋅

a

List all the factors for

x

2

,

a

1

,

x

1

,

a

2

to find the common factors.

x

2

=

x

⋅

x

a

1

=

a

x

1

=

x

a

2

=

a

⋅

a

The common factors for the variables

x

2

,

a

1

,

x

1

,

a

2

are

x

⋅

a

.

x

⋅

a

The GCF for the variable part is

x

a

.

GCF

Variable

=

x

a

Multiply the GCF of the numerical part

3

and the GCF of the variable part

x

a

.

3

x

a

Answer: 3xa

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor