The largest number which divides `70` and `125`, leaving remainder `5 and 8` respectively, is

Options

A. `13`
B. `65`
C. `875`
D. `1750`

Explanation

To find the largest number that divides 70 and 125, leaving remainders of 5 and 8 respectively, we can follow these steps:

### Step 1: Subtract the remainders from the original numbers
- For 70, subtract the remainder 5:
\[ 70 - 5 = 65 \]
- For 125, subtract the remainder 8:
\[ 125 - 8 = 117 \]

### Step 2: Find the greatest common divisor (GCD) of the two results
Now we need to find the GCD of 65 and 117.

### Step 3: Use the Euclidean algorithm to find the GCD
1. Divide 117 by 65 and find the remainder:
\[ 117 \div 65 = 1 \quad \text{(quotient)} \]
\[ 117 - (1 \times 65) = 52 \quad \text{(remainder)} \]

2. Now, take 65 and divide it by the remainder 52:
\[ 65 \div 52 = 1 \quad \text{(quotient)} \]
\[ 65 - (1 \times 52) = 13 \quad \text{(remainder)} \]

3. Next, take 52 and divide it by the remainder 13:
\[ 52 \div 13 = 4 \quad \text{(quotient)} \]
\[ 52 - (4 \times 13) = 0 \quad \text{(remainder)} \]

### Step 4: Conclusion
Since the last non-zero remainder is 13, the GCD of 65 and 117 is 13. Therefore, the largest number that divides 70 and 125, leaving remainders of 5 and 8 respectively, is:
\[ \boxed{13} \]