The image depicts a factor tree, which is used to find the prime factors of a number. Let's analyze and solve the problem step by step.
Step 1: Understand the Factor Tree
A factor tree breaks down a number into its prime factors. The top number (12 in this case) is decomposed into two factors, and each factor is further broken down until all the leaves of the tree are prime numbers.
Step 2: Analyze the Given Factor Tree
The factor tree is structured as follows:
- The top number is
12.
-
12 is decomposed into
2 and
6.
-
6 is further decomposed into
2 and
3.
- The numbers
2,
2, and
3 are all prime numbers.
Step 3: Verify the Prime Factorization
To ensure the factor tree is correct, we can multiply the prime factors back together to see if we get the original number:
\[
2 \times 2 \times 3 = 4 \times 3 = 12
\]
This confirms that the factor tree is correct.
Step 4: Identify the Prime Factors
The prime factors of
12 are the leaves of the factor tree:
\[
2, 2, 3
\]
Step 5: Write the Final Answer
The prime factorization of
12 is:
\[
12 = 2 \times 2 \times 3
\]
Or, using exponents:
\[
12 = 2^2 \times 3
\]
Final Answer:
\[
\boxed{2, 2, 3}
\]
Parent Tip: Review the logic above to help your child master the concept of prime factorization patterns.
