The work that Ryan did to find the greatest common factor of 48 and 72 is shown below.

Prime factorization of 48: 2, 2, 2, 2, 3

Prime factorization of 72: 2, 2, 2, 3, 3

The greatest common factor is 2 ' 2 ' 2 ' 2 ' 3 ' 3.

What is Ryan's error?

Ryan did not include all the common factors in the greatest common factor.

Ryan did not list all the factors in the prime factorization of 48.

Ryan did not list all the factors in the prime factorization of 72.

Ryan found the least common multiple.

(d) Ryan found the least common multiple.

Step-by-step explanation:

Here, the given numbers are: 48 and 72

Prime Factorizing the terms, we get:

48 = 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

Now, here Common Factor of 48 and 72 is 2, 2, 2, 3

So, Greatest Common Factor = 2 x 2 x 2 x 3 = 24

⇒ GCF of 48 and 72 is 24.

Also, LCM of 48 and 72 = 2 x 2 x 2 x 3 x 2 x 3 = 144

Now, consider all the given options:

(a) Ryan did not include all the common factors in the greatest common factor. FALSE he did include all the factors.

(b) Ryan did not list all the factors in the prime factorization of 48.

False, the prime factorization of 48 is correct.

(c) Ryan did not list all the factors in the prime factorization of 72.

False, the prime factorization of 72 is correct.

(d) Ryan found the least common multiple.

TRUE. LCM of the 48 and 72 is 2 ' 2 ' 2 ' 2 ' 3 ' 3 = 144