https://file.aiquickdraw.com/mathbot/file/1729355972101ep7bc38o.jpg

We are given the prime factorization of 28,728 as:

\[
28,728 = 2^3 \times 3^3 \times 7 \times 19
\]

Now, let's analyze each of the given numbers to check if they are factors of 28,728. A number is a factor if its prime factorization is a subset of the prime factorization of 28,728.

1. **63 = \(3^2 \times 7\):**
   - This matches part of the prime factorization of 28,728 since \(3^2\) and \(7\) are part of the factorization.
   - **63 is a factor.**

2. **16 = \(2^4\):**
   - The prime factorization of 28,728 contains \(2^3\), but 16 requires \(2^4\), which is more than we have.
   - **16 is not a factor.**

3. **8 = \(2^3\):**
   - This matches the \(2^3\) in the prime factorization of 28,728.
   - **8 is a factor.**

4. **38 = \(2 \times 19\):**
   - This exactly matches part of the prime factorization since \(2^1\) and \(19\) are included in 28,728's factorization.
   - **38 is a factor.**

5. **459 = \(3^3 \times 17\):**
   - While \(3^3\) is part of 28,728, the prime factorization of 28,728 does not include 17.
   - **459 is not a factor.**

### Conclusion:
The factors of 28,728 are:
- **63**
- **8**
- **38**

Would you like further details or have any questions? 

Here are five related questions:
1. How can you find the greatest common factor (GCF) of two numbers using their prime factorizations?
2. What is the difference between finding a factor and finding a multiple of a number?
3. How do prime factorizations help in simplifying fractions?
4. How can you use prime factorization to find the least common multiple (LCM) of two numbers?
5. What is the significance of prime factorization in cryptography?

**Tip:** When determining whether a number is a factor, always check if all prime factors of the number fit within the prime factorization of the larger number.

The prime factor decomposition of 28,728 is 2^3 × 3^3 × 7 × 19. Which of these numbers are factors of 28,728? The numbers are: 63 = 3^2 × 7, 16 = 2^4, 8 = 2^3, 38 = 2 × 19, 459 = 3^3 × 17.

Find out which numbers are factors of 28,728 using prime factor decomposition. Explore the prime factorization of 28,728 (2^3 × 3^3 × 7 × 19) and compare it with numbers like 63, 16, 8, 38, and 459. This problem is ideal for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation