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: Adjust the numbers by subtracting the remainders
- For the first number (70), subtract the remainder (5):
\[ 70 - 5 = 65 \]
- For the second number (125), subtract the remainder (8):
\[ 125 - 8 = 117 \]

### Step 2: Find the HCF (Highest Common Factor) of the adjusted numbers
We need to find the HCF of 65 and 117.

### Step 3: Prime factorization of 65
- 65 can be factored as:
\[ 65 = 5 \times 13 \]

### Step 4: Prime factorization of 117
- 117 can be factored as:
\[ 117 = 3 \times 39 \]
- Further factor 39:
\[ 39 = 3 \times 13 \]
- Thus, the complete factorization of 117 is:
\[ 117 = 3^2 \times 13 \]

### Step 5: Identify the common factors
- The prime factors of 65 are \(5\) and \(13\).
- The prime factors of 117 are \(3^2\) and \(13\).
- The common factor is \(13\).

### Step 6: Conclusion
The largest number that divides both 70 and 125, leaving remainders of 5 and 8 respectively, is:
\[ \text{HCF} = 13 \]

### Final Answer
The largest number is **13**.

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