Three sets of physics, chemistry and mathematics books have to be stacked in such a way that all the books are stored topic wise and the number of books in each stack is the same. The number of physics books is 192, the number of chemistry books is 240 and the number of mathematics books is 168. Determine the number of stacks of physics, chemistry and mathematics books.

The problem is asking for the number of stacks that can be made where the books of each subject (Physics, Chemistry, Mathematics) are stored separately and evenly across all stacks. To find this, we need to determine the greatest common divisor (GCD) of the number of books for each subject, as the GCD will give us the largest number of stacks such that the books can be evenly divided among them.

The number of books in each subject is:
- Physics: 192 books
- Chemistry: 240 books
- Mathematics: 168 books

### Step 1: Find the GCD of the three numbers.

We will use the Euclidean algorithm to calculate the GCD step by step.

#### Step 2: Find GCD of Physics and Chemistry books.
- GCD(192, 240):

First, divide 240 by 192 and get the remainder:
\[
240 \div 192 = 1 \text{ (remainder } 240 - 192 = 48\text{)}
\]
Now, find the GCD of 192 and 48:
\[
192 \div 48 = 4 \text{ (remainder } 192 - 192 = 0\text{)}
\]
Thus, GCD(192, 240) = 48.

#### Step 3: Find the GCD of the result and Mathematics books.
- GCD(48, 168):

Now, divide 168 by 48 and get the remainder:
\[
168 \div 48 = 3 \text{ (remainder } 168 - 144 = 24\text{)}
\]
Now, find the GCD of 48 and 24:
\[
48 \div 24 = 2 \text{ (remainder } 48 - 48 = 0\text{)}
\]
Thus, GCD(48, 168) = 24.

### Step 4: Conclusion
The GCD of 192, 240, and 168 is 24. This means the books can be divided into **24 stacks**.

### Number of books per stack:
- Physics: \(192 \div 24 = 8\) books per stack
- Chemistry: \(240 \div 24 = 10\) books per stack
- Mathematics: \(168 \div 24 = 7\) books per stack

Thus, the number of stacks is **24**.

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Would you like more details or have any questions? Here are 5 related questions you can explore:

1. How would you find the least common multiple (LCM) of the three numbers instead of the GCD?
2. Can you apply this GCD method to dividing other resources evenly, such as time or material?
3. What is the significance of the Euclidean algorithm in real-life applications?
4. What are other methods to find the GCD of large numbers quickly?
5. How does this approach differ from finding the number of unique ways to arrange the books?

**Tip:** The Euclidean algorithm is a highly efficient way to compute the GCD of two numbers and can be applied repeatedly for larger sets of numbers!

Determine how to stack 192 physics, 240 chemistry, and 168 mathematics books evenly using the greatest common divisor (GCD). This problem utilizes number theory and the Euclidean algorithm to find the GCD, suitable for students in Grades 8-10.

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