The factor tree method is a technique used to break down a number into its prime factors. Here's how you can use the factor tree method for a three-digit number:

Steps to Perform the Factor Tree Method:

1. Choose a Starting Factor:

   • Begin by selecting any two factors of the number (other than 1 and the number itself).
   • These factors should multiply to give the original number.

2. Break Down the Factors:

   • If either of the factors is not a prime number, break it down further into its own factors.
   • Continue breaking down until all the factors are prime numbers.

3. Prime Factorization:

   • The prime factors are the "leaves" of your factor tree, i.e., the numbers at the ends of each branch.
   • Multiply all the prime factors together, and they should give you the original number.

Example: Factor Tree of 180

1. Start with the number 180:

   • Choose two factors: $180 = 2 \times 90$

2. Break Down 90:

   • $90 = 2 \times 45$

3. Break Down 45:

   • $45 = 3 \times 15$

4. Break Down 15:

   • $15 = 3 \times 5$

5. Complete Factor Tree:

   • The factor tree for 180 is:

          180
         /   \
        2    90
            /  \
           2   45
              /  \
             3   15
                /  \
               3    5
     

   • Prime factors: $2 \times 2 \times 3 \times 3 \times 5$
   • Simplified as $2^2 \times 3^2 \times 5$

Prime Factorization of 180:

$180 = 2^2 \times 3^2 \times 5$

General Tips:

• Always start with the smallest prime number (2, 3, 5, etc.) if possible.
• A factor tree can be done in several ways, but the prime factors will always be the same.

Do you want details on any specific part, or do you have any questions?

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Here are 8 related questions that might expand your understanding:

1. What is the prime factorization of 256 using the factor tree method?
2. How do you factorize a number like 210 using the factor tree method?
3. Can you explain the difference between a factor tree and a prime factorization?
4. What are the prime factors of 84 using the factor tree method?
5. How do you determine the least common multiple (LCM) using prime factors?
6. What is the significance of prime numbers in the factor tree method?
7. How can you use the factor tree method to simplify fractions?
8. What is the prime factorization of 1000 using the factor tree method?

Tip: Always check if a number is divisible by smaller primes (like 2, 3, 5) to start your factor tree more easily.