Find the greatst number that divides 556, 763 and 349 and leaves 4 as remainders respectively.

Options

A. 69
B. 92
C. 36
D. 54

Answer

To find the greatest number that divides 556, 763, and 349 while leaving a remainder of 4, we can follow these steps:

### Step-by-Step Solution:

1. **Subtract the Remainder from Each Number**:
Since we need the number to leave a remainder of 4, we first subtract 4 from each of the given numbers.
- For 556:
\[ 556 - 4 = 552 \]
- For 763:
\[ 763 - 4 = 759 \]
- For 349:
\[ 349 - 4 = 345 \]

2. **List the New Numbers**:
After subtraction, we have the numbers:
- 552
- 759
- 345

3. **Find the Highest Common Factor (HCF)**:
Now, we need to find the HCF of the numbers 552, 759, and 345.

4. **Factorize Each Number**:
- **For 552**:
\[ 552 = 2^3 \times 69 \]
- **For 759**:
\[ 759 = 11 \times 69 \]
- **For 345**:
\[ 345 = 5 \times 69 \]

5. **Identify the Common Factors**:
The common factor among the three numbers is 69.

6. **Conclusion**:
Therefore, the greatest number that divides 556, 763, and 349 and leaves a remainder of 4 is:
\[ \text{HCF} = 69 \]

### Final Answer:
The greatest number is **69**.