Question

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

Prime factorization of 48: 2 x 2 x 2 x 2 x 3
Prime factorization of 72: 2 x 2 x 2 x 3 x 3

The greatest common factor is 2 ´ 2 ´ 2 ´ 3 x 3

What is Ryan’s error?

Answer 1

Answer: See explanation

Explanation:

Prime factorization of 48: 2 x 2 x 2 x 2 x 3

Prime factorization of 72: 2 x 2 x 2 x 3 x 3

Ryan should first make sure there are the same number of 2s and 3s. To make myself more clear, I'm dividing 48 by 2 and 72 by 3 to get:

48/2: 2*2*2*3

72/3: 2*2*2*3

Now solve for 2*2*2*3 which would give you 24.

However, Ryan's answer was 2*2*2*3*3 which is 72. 72 Isn't a factor of 48.