The prime factorizations of 16 and 24 are shown below. prime factorization of 16: 2, 2, 2, 2 prime factorization of 24: 2, 2, 2, 3 using the prime factorizations, what is the greatest common factor of 16 and 24? 1. 2 2. 2 ´ 2 3. 2 ´ 2 ´ 2 4. 2 ´ 2 ´ 2 ´ 2 ´ 3

3

Step-by-step explanation:

given the prime factors of 16 and 24

Then the greatest common factor of both is the number of factors common to both, that is

2, 2, 2 = 2 × 2 × 2 = 8

The greatest common factor (GCF) is 2,2,2 or  8

Step-by-step explanation:

To find the GCF of two numbers you first need the prime factorization of both numbers that, in this case is given. Then you must find the number of common prime factors in both factorizations and construct pairs in this manner:

Prime fact 16 : 2,2,2,2

Prime fact 24 = 2,2,2,3

16 has as first prime factor 2. Number 24 also has a 2 as prime factor so 2 is a common factor: First common factor = 2. Now lets see the following factors:

Prime fact 16 : 2,2,2,2

Prime fact 24 = 2,2,2,3

GCF until now = 2

The second prime factor of 16 is 2 and of 24 is also 2 so the GCF has another 2.

Prime fact 16 : 2,2,2,2

Prime fact 24 = 2,2,2,3

GCF until now = 2,2

The third number of 16 and 24 is also 2. We take also this pair:

GCF until now = 2,2,2

The fourth prime factor of 16 is 2 but the one of 24 is 3 so this factor is not common. Now that we have revised both prime factorizations the final answer is

GCF=2,2,2 which we multiply to obtain 2*2*2 = 8