The problem requires us to match linear expressions with their greatest common factor (GCF). The linear expressions are $32p - 20$, $7 - 63c$, $12n - 36$, and $9cd - 27c$. The possible GCFs are $12$, $4$, $9c$, and $7$.

1. Problem Description

The problem requires us to match linear expressions with their greatest common factor (GCF). The linear expressions are $32p - 20$, $7 - 63c$, $12n - 36$, and $9cd - 27c$. The possible GCFs are $12$, $4$, $9c$, and $7$.

2. Solution Steps

We need to find the GCF for each linear expression.

* For $32p - 20$:

Factors of 32 are 1, 2, 4, 8, 16,

3

2. Factors of 20 are 1, 2, 4, 5, 10,

2

0. The greatest common factor is

4.

* For $7 - 63c$:

Factors of 7 are 1,

7. Factors of 63 are 1, 3, 7, 9, 21,

6

3. The greatest common factor is

7.

* For $12n - 36$:

Factors of 12 are 1, 2, 3, 4, 6,

1

2. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18,

3

6. The greatest common factor is

1

2.

* For $9cd - 27c$:

Factors of 9 are 1, 3,

9. Factors of 27 are 1, 3, 9,

2

7. Both terms have $c$.

So the greatest common factor is $9c$.

Therefore:

$32p - 20$ matches with $GCF = 4$.

$7 - 63c$ matches with $GCF = 7$.

$12n - 36$ matches with $GCF = 12$.

$9cd - 27c$ matches with $GCF = 9c$.

3. Final Answer

$32p-20$ matches $GCF = 4$

$7-63c$ matches $GCF = 7$

$12n-36$ matches $GCF = 12$

$9cd-27c$ matches $GCF = 9c$