Latoya created a factor tree and wrote the prime factorization of 90 shown below.

Question

A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5.
What is Latoya’s error?
She should not have found the factors of 9.
She should have included an exponent of 2 on the 3.
She should have included 9 and 10 in the prime factorization.
She should have started the tree with 2 times 45.

Answer 1

Latoya's error lies in the prime factorization of 90. In her factor tree, she correctly breaks down 90 into 9 and 10, but when breaking down those factors, she fails to represent the prime factorization correctly.

The prime factorization of 90 is:

1. Starting with 90, we can indeed break it down into 9 and 10.
2. The factor 9 can be broken down into 3 and 3, which means \(3\) is a factor twice (or \(3^2\)).
3. The factor 10 can be broken down into 2 and 5.

So, the correct prime factorization of 90 should be:

\[ 90 = 2 \times 3^2 \times 5 \]

Thus, Latoya's error is that she should have included an exponent of 2 on the 3.