Manuel created a factor tree and wrote the prime factorization of 60 shown below.

Question

A factor tree of 60. 60 branches to 4 and 15. 15 branches to 3 and 5. The equation is 60 = 3 times 4 times 5.
What is Manuel’s error?
He did not include 15 in the prime factorization.
He did not find the prime factors of 4.
He should have started the factor tree with 2 times 30.
He should not have found the factors of 15.

Answer 1

Manuel's error in his factor tree and prime factorization of 60 lies in the fact that he did not find the prime factors of 4.

The correct prime factorization of 60 should include the prime factors of all branches. Since 4 can be further broken down into 2 times 2 (which are both prime), the full prime factorization of 60 should be:

60 = 2 × 2 × 3 × 5, or expressed in exponential form: 60 = 2² × 3 × 5.

Therefore, the correct answer is: He did not find the prime factors of 4.