To find the prime factorization of 507 using a factor tree, follow these steps:

1. Divide 507 by the smallest prime number:

   • 507 is odd, so it's not divisible by 2. Let's try dividing by 3:
   • $507 \div 3 = 169$

2. Factor 169:

   • 169 is not divisible by 2 or 3, but it is divisible by 13:
   • $169 \div 13 = 13$

3. Prime factorization:

   • 13 is a prime number, so we cannot factor it further.

The factor tree looks like this:

    507
   /   \
  3     169
       /   \
      13    13

So, the prime factorization of 507 is:

$507 = 3 \times 13 \times 13 = 3 \times 13^2$

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the prime factorization of 169?
2. How do you determine if a number is divisible by 3?
3. What is the prime factorization of 338?
4. How can you find the prime factorization of a large number efficiently?
5. How do you verify that the factorization is correct?

Tip: When using a factor tree, always start with the smallest prime number and work your way up.