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**Problem 26**:  
Three sets of English, Hindi, and Mathematics books have to be stacked such that all books are stored topic-wise, and the height of each stack is the same. The number of English books is 96, Hindi books is 240, and Mathematics books is 336. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi, and Mathematics books.

### Solution:

We are asked to find the number of stacks for each subject so that the height of the stacks is the same. This problem boils down to finding the greatest common divisor (GCD) of the three numbers: 96, 240, and 336.

1. **Prime factorization**:
   - \( 96 = 2^5 \times 3 \)
   - \( 240 = 2^4 \times 3 \times 5 \)
   - \( 336 = 2^4 \times 3 \times 7 \)

2. **Find the GCD**:
   The common prime factors are \( 2^4 \times 3 \). Therefore, the GCD is:
   \[
   \text{GCD} = 2^4 \times 3 = 16 \times 3 = 48
   \]

Thus, the greatest number of stacks where the height of each stack is equal is **48**.

3. **Number of stacks for each subject**:
   - English books: \( \frac{96}{48} = 2 \)
   - Hindi books: \( \frac{240}{48} = 5 \)
   - Mathematics books: \( \frac{336}{48} = 7 \)

Therefore, there will be 2 stacks of English books, 5 stacks of Hindi books, and 7 stacks of Mathematics books.

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Let me know if you'd like further details on this or help with other problems! Here are some related questions to help you practice:

1. What is the least common multiple (LCM) of 96, 240, and 336?
2. If the number of English books were 120, how many stacks would there be for equal stack height?
3. What if the thickness of books varied between subjects—how would you approach the problem?
4. Can you determine a formula for the number of stacks for any given set of book counts?
5. What is the total height of one stack if each book has a thickness of 1.5 cm?

**Tip**: Prime factorization is a very useful tool for finding both GCD and LCM, especially for problems involving divisibility.

Three sets of English, Hindi, and Mathematics books have to be stacked such that all books are stored topic-wise, and the height of each stack is the same. The number of English books is 96, Hindi books is 240, and Mathematics books is 336. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi, and Mathematics books.

Learn how to determine the number of stacks for English, Hindi, and Math books using the greatest common divisor (GCD). This problem involves finding the GCD of 96, 240, and 336 through prime factorization and is suitable for Grade 10 students.

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