Question

Factor each by using the GCF. a) 36x+81 b) 24a+36

Answer 1

To find the GCF of numbers.

1. Find the prime factorizations of the numbers.

2. The GCF is the product of the common factors with lower exponent.

a. 36x + 81

Let's start with the prime factorizations.

36 = 2^2 * 3^2

81 = 3^4

The only factor in common is 3. There is a 3^2 and a 3^4. We use 3^2 since it has a lower exponent.

GCF = 3^2 = 9

36x + 81 = 9(4x + 9)

b. 24a + 36

Let's start with the prime factorizations.

24 = 2^3 * 3

36 = 2^2 * 3^2

The two numbers have factor 2 in common. There is a 2^2 and a 2^3, so use 2^2 since it has the lower exponent.

The two numbers have factor 3 in common. There is a 3^2 and a 3. Use 3 since it has the lower exponent.

GCF = 2^2 * 3 = 4 * 3 = 12

24a + 36 = 12(2a + 3)

Answer 2

The Greatest Common Factor (GCF) is very important when factoring. Later on, you will forget to pull out a GCF and the answer will be wrong. Always look for a GCF before doing anything.

Let's try factoring these:

a.) $36x+81$

The greatest common factor of this expression is 9, because it is the maximum number that both can go into. Let's solve.

$9(4x+9)$

This is the simplest this expression can get. This would be your final answer. Let's try the other one.

b.) $24a+36$

The GCF of this one is 12. Let's simplify it.

$12(2a+3)$

This is also the simplest you can get it. You can do nothing further. So, your final answers are:

a.) $9(4x+9)$

b.) $12(2a+3)$