The greatest number which, when divided by 641, 711 and 1527 leaves the remainder 12, 8 and 10 respectively, is

Options

A. 17
B. 26
C. 37
D. 47

Answer

To find the greatest number which, when divided by 641, 711, and 1527 leaves the remainders 12, 8, and 10 respectively, we can follow these steps:

### Step 1: Adjust the Divisors
Since we need to find a number that leaves specific remainders when divided, we first adjust the divisors by subtracting the respective remainders from each number.

- For 641, the adjusted number is:
\[ 641 - 12 = 629 \]

- For 711, the adjusted number is:
\[ 711 - 8 = 703 \]

- For 1527, the adjusted number is:
\[ 1527 - 10 = 1517 \]

### Step 2: Find the HCF of the Adjusted Numbers
Next, we need to find the Highest Common Factor (HCF) of the adjusted numbers: 629, 703, and 1517.

1. **Factorization of 629**:
\[ 629 = 17 \times 37 \]

2. **Factorization of 703**:
\[ 703 = 19 \times 37 \]

3. **Factorization of 1517**:
\[ 1517 = 41 \times 37 \]

### Step 3: Identify the Common Factor
Now, we look for the common factors among the three numbers. The only common factor from the factorizations is:
\[ 37 \]

### Step 4: Conclusion
Thus, the greatest number that satisfies the conditions of the problem is:
\[ \text{Greatest number} = 37 \]