The greatest number that will divide 187,233 and 279 leaving the same remainder in each case is

Options

A. 49
B. 54
C. 46
D. 36

Answer

To find the greatest number that will divide 187, 233, and 279 leaving the same remainder in each case, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find a number \( N \) such that when we divide 187, 233, and 279 by \( N \), they all leave the same remainder \( R \). This means that \( 187 - R \), \( 233 - R \), and \( 279 - R \) must all be divisible by \( N \).

2. **Setting Up the Equations**:
If we subtract \( R \) from each number, we can express the problem in terms of differences:
- \( 187 - R \)
- \( 233 - R \)
- \( 279 - R \)

We can ignore \( R \) for now, as it will cancel out when we find the differences.

3. **Finding the Differences**:
Calculate the differences between the numbers:
- \( 233 - 187 = 46 \)
- \( 279 - 233 = 46 \)

4. **Finding the HCF**:
Now, we need to find the highest common factor (HCF) of these differences:
- The differences we have are 46 and 46.
- The HCF of 46 and 46 is simply 46.

5. **Conclusion**:
Therefore, the greatest number that will divide 187, 233, and 279 leaving the same remainder in each case is **46**.

### Final Answer:
The greatest number is **46**.