Find the prime factorization of
507
using a factor tree.

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.

Learn how to find the prime factorization of 507 using a factor tree method. Follow a step-by-step explanation including division by primes and factoring of resulting numbers. Suitable for students in Grades 6-8.

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