The image shows a
factor tree for the number 32, which is used to find its prime factorization. Let's break down the solution step by step:
Step 1: Understanding the Factor Tree
A factor tree is a diagram that helps us decompose a number into its prime factors. The process involves:
1. Starting with the given number (in this case, 32).
2. Breaking it down into two factors.
3. Continuing to break down each non-prime factor until all factors are prime numbers.
Step 2: Analyzing the Given Factor Tree
The factor tree in the image starts with 32 at the top. It is broken down as follows:
-
32 is split into
4 and
8.
-
4 is further split into
2 and
2.
-
8 is further split into
2 and
4.
-
4 (from the right branch) is further split into
2 and
2.
Step 3: Identifying the Prime Factors
From the factor tree:
- The leaves of the tree (the numbers at the bottom) are all
prime numbers.
- The prime factors of 32 are:
2, 2, 2, 2, 2.
Step 4: Writing the Prime Factorization
The prime factorization of 32 is the product of these prime factors:
\[
32 = 2 \times 2 \times 2 \times 2 \times 2
\]
Step 5: Verifying the Solution
To verify, we multiply the prime factors back together:
\[
2 \times 2 = 4
\]
\[
4 \times 2 = 8
\]
\[
8 \times 2 = 16
\]
\[
16 \times 2 = 32
\]
This confirms that the prime factorization is correct.
Final Answer
The prime factorization of 32 is:
\[
\boxed{2 \times 2 \times 2 \times 2 \times 2}
\]
Parent Tip: Review the logic above to help your child master the concept of factor tree prime factorization of 45.
