2. Which factor tree shows the correct prime factorization of 12?
To determine the prime factorization of a number, we can use a factor tree. It's a method of breaking down the number into its prime factors.
To find the prime factorization of 12, we start by dividing it by its smallest prime factor, which is 2.
First Factor Tree (incorrect):
12
/ \
2 6
/ \
3 2
In this factor tree, we cannot continue dividing 6 because it is not divisible by 2. So, we try dividing by the next smallest prime factor, which is 3.
Second Factor Tree (correct):
12
/ \
3 4
/ \
2 2
In this factor tree, both branches of the tree end with prime numbers (3, 2, 2), and there are no further divisions possible. Therefore, the correct prime factorization of 12 is 2 * 2 * 3, or 2^2 * 3.
The factor tree that correctly shows the prime factorization of 12 is the second factor tree.