Which same number should be multiplied to 231 and 596, so that both products are equal?

Options

A. 2
B. 3
C. 1
D. 0

Explanation

To find the same number that should be multiplied to both 231 and 596 so that both products are equal, we can denote the unknown number as \( k \). We need to set up the equation based on the problem statement:

1. **Set up the equation**:
\[ 231 \times k = 596 \times k \]

2. **Rearrange the equation**:
To solve for \( k \), we can rearrange the equation:
\[ 231k - 596k = 0 \]
This simplifies to:
\[ (231 - 596)k = 0 \]

3. **Calculate \( 231 - 596 \)**:
\[ 231 - 596 = -365 \]
So, we have:
\[ -365k = 0 \]

4. **Solve for \( k \)**:
The only solution to this equation is:
\[ k = 0 \]

5. **Conclusion**:
Thus, the same number that should be multiplied to both 231 and 596 so that both products are equal is \( k = 0 \).