If B is greater than A, what is B in AB x BA = 1729?

Given that \( AB \times BA = 1729 \), where \( A \) and \( B \) are digits and \( B \) is greater than \( A \), let's analyze the problem.

### Step 1: Interpret the problem.
- \( AB \) means a two-digit number with \( A \) as the tens digit and \( B \) as the units digit. Therefore, \( AB = 10A + B \).
- \( BA \) is another two-digit number with \( B \) as the tens digit and \( A \) as the units digit. Therefore, \( BA = 10B + A \).

The equation becomes:
\[
(10A + B) \times (10B + A) = 1729
\]

### Step 2: Factorize 1729.
To solve this, we first factorize 1729:
\[
1729 = 7 \times 13 \times 19
\]
Since we need two factors that could correspond to \( AB \) and \( BA \) being two-digit numbers, let's try possible combinations of these factors.

### Step 3: Test possible values.
Let's test the pairs:

1. \( 19 \times 91 = 1729 \)
2. \( 13 \times 133 = 1729 \) (Not valid since 133 is not a two-digit number.)
3. \( 7 \times 247 = 1729 \) (Not valid since 247 is not a two-digit number.)

So, the valid pair is \( 19 \times 91 = 1729 \).

### Step 4: Identify \( A \) and \( B \).
In \( 19 \), \( A = 1 \) and \( B = 9 \).

In \( 91 \), \( B = 9 \) and \( A = 1 \).

So, \( B = 9 \).

### Conclusion
The value of \( B \) is **9**.

Would you like more details or have any other questions? Here are some related questions to consider:

1. How can we verify the factorization of larger numbers systematically?
2. What is the significance of the number 1729 in mathematics?
3. How does digit multiplication differ from regular multiplication?
4. What are other examples of mathematical puzzles involving digits?
5. How does this problem relate to number theory?

**Tip:** Factorization is a powerful tool for solving digit puzzles. Always check the product's factor pairs first.

Explore how to solve the equation AB x BA = 1729, where A and B are digits, and B is greater than A. Discover the method for identifying the digits A and B and understand the factorization approach used in solving such problems. Suitable for students in Grades 6-8.

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