The sum of three consecutive odd natural numbers is 69. Find the prime number out of these
numbers.

Let the three consecutive odd natural numbers be \(x\), \(x + 2\), and \(x + 4\).

The sum of these three numbers is given as 69. So, we can write the equation:

\[
x + (x + 2) + (x + 4) = 69
\]

Simplifying the equation:

\[
x + x + 2 + x + 4 = 69
\]

\[
3x + 6 = 69
\]

Subtract 6 from both sides:

\[
3x = 63
\]

Divide both sides by 3:

\[
x = 21
\]

So, the three consecutive odd numbers are:

\[
21, 23, \text{and } 25
\]

Now, we need to identify the prime number among these. 

- **21** is not a prime number (divisible by 3 and 7).
- **23** is a prime number.
- **25** is not a prime number (divisible by 5).

Thus, the prime number out of these three numbers is **23**.

### Answer: 
The prime number among the three consecutive odd natural numbers is **23**.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. What are the next three consecutive odd numbers after 25?
2. How can we determine if a number is prime?
3. Can the sum of three consecutive even numbers also be a prime?
4. What is the sum of four consecutive odd numbers that starts with 15?
5. How do we solve for three consecutive even numbers with a given sum?

**Tip:** To find a prime number quickly, check if it's divisible by any prime number smaller than its square root.

Learn how to find the prime number among three consecutive odd natural numbers whose sum is 69. This problem involves arithmetic sequences and prime number identification. Suitable for students in Grades 6-8.

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