To find the prime factorization of 45 using a factor tree, we start by dividing it by the smallest prime number.

Here’s how you can do it:

1. Start with 45. The smallest prime number that divides 45 is 3. $45 \div 3 = 15$

2. Next, divide 15 by the smallest prime number, which is also 3. $15 \div 3 = 5$

3. Now, 5 is a prime number, so we stop here.

The prime factorization of 45 is: $45 = 3 \times 3 \times 5$

Or, in exponential form: $45 = 3^2 \times 5$

If you want, I can also create a visual factor tree of this! Would you like that?

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Would you like more details or have any questions?
Here are 5 related questions you might want to explore:

1. How do you find the prime factorization of 60?
2. What is the least common multiple (LCM) of 45 and 30 using prime factors?
3. How can prime factorization help in finding the greatest common divisor (GCD)?
4. Why is 1 not considered a prime number?
5. How can factor trees be used to simplify fractions?

Tip: Always start with the smallest prime number when creating a factor tree to make factorization easier!