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We are asked to determine which of the five numbers are factors of 28,728 based on its prime factor decomposition.

The prime factor decomposition of 28,728 is:
\[
28,728 = 2^3 \times 3^3 \times 7 \times 19
\]

Now, we need to check each number's prime factorization and see if they divide 28,728 without leaving any remainder.

### 1. \( 63 = 3^2 \times 7 \)
- The prime factorization of 63 includes \(3^2\) and \(7\). These primes are all present in 28,728, and \(3^2\) and \(7\) do not exceed the powers in 28,728's prime factorization.
- **63 is a factor of 28,728**.

### 2. \( 16 = 2^4 \)
- The prime factorization of 16 includes \(2^4\), but 28,728 only has \(2^3\). Since \(2^4\) exceeds \(2^3\), 16 is **not** a factor of 28,728.

### 3. \( 8 = 2^3 \)
- The prime factorization of 8 is \(2^3\), and 28,728 contains \(2^3\), so \(8\) is a factor of 28,728.
- **8 is a factor of 28,728**.

### 4. \( 459 = 3^3 \times 17 \)
- The prime factorization of 459 includes \(3^3\) and 17. However, 28,728 does not contain 17 as a prime factor. 
- **459 is not a factor of 28,728**.

### 5. \( 38 = 2 \times 19 \)
- The prime factorization of 38 includes \(2\) and \(19\), and both primes are present in 28,728 with sufficient powers.
- **38 is a factor of 28,728**.

### Correct answers:
- 63
- 8
- 38

Would you like more details or have any questions?

### Related questions:
1. How do you find the prime factorization of large numbers like 28,728?
2. Why does \(16 = 2^4\) not divide 28,728?
3. How do you verify if a number is a factor of another using prime factorizations?
4. What are the general rules for finding factors of a number?
5. Can a composite number with different primes be a factor of another composite number?

### Tip:
When checking for factors using prime factorizations, ensure that each prime factor in the smaller number has an equal or lesser power than in the larger number.

Which of these numbers are factors of 28,728?

Learn how to determine which numbers are factors of 28,728 using its prime factorization (2^3 × 3^3 × 7 × 19). This solution walks through the prime factorizations of 63, 16, 8, 459, and 38 and explains which numbers divide 28,728.

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