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To solve the problem, let's denote the two consecutive odd natural numbers as \( x \) and \( x + 2 \). According to the question, their product is 143:

\[
x(x + 2) = 143
\]

Expanding the equation gives:

\[
x^2 + 2x = 143
\]

Rearrange it into a standard quadratic equation:

\[
x^2 + 2x - 143 = 0
\]

Now, we can solve this quadratic equation using the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

where \( a = 1 \), \( b = 2 \), and \( c = -143 \). Plugging in these values, we get:

\[
x = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-143)}}{2(1)}
\]

\[
x = \frac{-2 \pm \sqrt{4 + 572}}{2}
\]

\[
x = \frac{-2 \pm \sqrt{576}}{2}
\]

\[
x = \frac{-2 \pm 24}{2}
\]

This results in two possible solutions:

1. \( x = \frac{22}{2} = 11 \)
2. \( x = \frac{-26}{2} = -13 \) (not a natural number)

So, the two consecutive odd natural numbers are \( 11 \) and \( 13 \). The largest number among them is:

\[
\boxed{13}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How can you solve quadratic equations using factorization instead of the quadratic formula?
2. What are some methods to check if a number is odd or even?
3. Can you solve for two consecutive even natural numbers that have a given product?
4. How can you derive the quadratic formula step by step?
5. What are the properties of natural numbers, and how do they differ from whole numbers?

**Tip:** Always check the feasibility of your solutions, especially when dealing with word problems that specify "natural numbers" or "integers."

The product of two consecutive odd natural numbers is 143. Find the largest number among them.

This problem requires solving for two consecutive odd natural numbers whose product is 143. The solution involves applying the quadratic equation formula and identifying the largest of the two numbers, suitable for students in Grades 7-9.

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