https://file.aiquickdraw.com/mathbot/file/1726264071736j4v63s2v.jpg

Let's analyze the clues one by one:

1. **Clue 1: My number is a perfect square.**
   - The number must be a perfect square, meaning it can be expressed as \( n^2 \), where \( n \) is an integer.

2. **Clue 2: The only prime number in its prime factorization is 2.**
   - This means that the number is a power of 2, as no other prime numbers are involved in its factorization.

3. **Clue 3: My number is a factor of 32.**
   - The possible factors of 32 are: 1, 2, 4, 8, 16, and 32.

4. **Clue 4: The sum of its digits is odd.**
   - We need to find a number from the possible factors whose digits add up to an odd number.

### Perfect squares among the factors of 32:
- The factors of 32 are 1, 2, 4, 8, 16, and 32. Among these, the perfect squares are 1, 4, and 16.

Now, let's apply the other clues:
- The prime factorization must only include 2, which is true for all of these numbers (1, 4, 16).
- The sum of the digits:
   - \( 1 \): Sum = 1 (odd).
   - \( 4 \): Sum = 4 (even).
   - \( 16 \): Sum = 1 + 6 = 7 (odd).

### Conclusion:
The number is **16**, as it satisfies all four clues.

Do you want more details or have any further questions?

Here are 5 related questions to explore:

1. What are the first 10 perfect squares?
2. How can prime factorization be used to identify properties of a number?
3. What other numbers have the sum of their digits as odd?
4. How many factors does 32 have, and how do we calculate them?
5. What other numbers are perfect squares and factors of powers of 2?

**Tip:** A number's prime factorization is helpful to determine if it is a power of a prime, like powers of 2, 3, etc.

What is my number? Clue 1: My number is a perfect square. Clue 2: The only prime number in its prime factorization is 2. Clue 3: My number is a factor of 32. Clue 4: The sum of its digits is odd.

Explore how to find a number that is a perfect square, whose only prime factor is 2, and is a factor of 32. This problem involves using prime factorization, properties of perfect squares, and rules about digit sums. Suitable for Grades 5-7.

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