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

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)