Find the greatest number that divides 80 and 115 leaving remainder 8 and 7 respectively.

Options

A. 34
B. 38
C. 31
D. 36

Explanation

To find the greatest number that divides 80 and 115 leaving remainders of 8 and 7 respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the numbers and their remainders**:
- We have two numbers: 80 and 115.
- The remainders when these numbers are divided by the unknown greatest number are 8 and 7 respectively.

2. **Adjust the numbers by subtracting the remainders**:
- For 80, subtract the remainder 8:
\[ 80 - 8 = 72 \]
- For 115, subtract the remainder 7:
\[ 115 - 7 = 108 \]

3. **Find the greatest common divisor (GCD) or highest common factor (HCF)**:
- Now, we need to find the HCF of the adjusted numbers 72 and 108.

4. **Use the division method to find the HCF**:
- Divide 108 by 72:
\[ 108 \div 72 = 1 \quad \text{(remainder 36)} \]
- Now take the divisor (72) and the remainder (36) and repeat the process:
\[ 72 \div 36 = 2 \quad \text{(remainder 0)} \]
- Since the remainder is now 0, the last non-zero remainder (36) is the HCF.

5. **Conclusion**:
- The greatest number that divides both 80 and 115, leaving remainders of 8 and 7 respectively, is **36**.

### Final Answer:
The greatest number is **36**.