Based on the provided image, which shows a "Factor Trees" worksheet and its corresponding answer key, the task is to find the prime factorization of several numbers using a factor tree method. A factor tree is a diagram used to break down a number into its prime factors by repeatedly dividing it into pairs of factors until only prime numbers remain.
Here is the solution for each number shown on the worksheet, based on the completed examples in the answer key:
1. For the number 20:
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Factor Tree Breakdown:
* Start with 20 at the top.
* Break 20 into 4 and 5.
* Break 4 into 2 and 2.
* The prime factors are 2, 2, and 5.
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Prime Factorization: $20 = 2 \times 2 \times 5$, which can be written in exponential form as $20 = 2^2 \times 5$.
2. For the number 36:
*
Factor Tree Breakdown:
* Start with 36 at the top.
* Break 36 into 6 and 6.
* Break each 6 into 2 and 3.
* The prime factors are 2, 2, 3, and 3.
*
Prime Factorization: $36 = 2 \times 2 \times 3 \times 3$, which can be written in exponential form as $36 = 2^2 \times 3^2$.
3. For the number 100:
*
Factor Tree Breakdown:
* Start with 100 at the top.
* Break 100 into 50 and 2.
* Break 50 into 25 and 2.
* Break 25 into 5 and 5.
* The prime factors are 2, 2, 5, and 5.
*
Prime Factorization: $100 = 2 \times 2 \times 5 \times 5$, which can be written in exponential form as $100 = 2^2 \times 5^2$.
In summary, the solution involves constructing a factor tree for each number by finding factor pairs and continuing to break down composite numbers until all branches end in prime numbers. The final step is to write the product of these prime numbers, which is the prime factorization of the original number.
Parent Tip: Review the logic above to help your child master the concept of 5th grade factor trees.
