Find the largest number that divides 32 and 99 having leaving remainder 5 and 8 respectively.

Answer

To solve the problem of finding the largest number that divides 32 and 99 leaving remainders of 5 and 8 respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Subtract the Remainders from the Given Numbers**:
- From 32, subtract the remainder 5:
\[ 32 - 5 = 27 \]
- From 99, subtract the remainder 8:
\[ 99 - 8 = 91 \]

2. **Identify the Numbers**:
- We now have two numbers: 27 and 91.

3. **Find the Prime Factorization of Both Numbers**:
- For 27:
\[ 27 = 3 \times 3 \times 3 = 3^3 \]
- For 91:
\[ 91 = 7 \times 13 \]

4. **Determine the Common Factors**:
- The prime factorization of 27 is \(3^3\).
- The prime factorization of 91 is \(7 \times 13\).
- There are no common prime factors between 27 and 91.

5. **Find the Highest Common Factor (HCF)**:
- Since there are no common factors, the HCF of 27 and 91 is 1.

6. **Conclusion**:
- The largest number that divides both 32 and 99 leaving remainders of 5 and 8 respectively is:
\[ \text{HCF} = 1 \]

### Final Answer:
The largest number that divides 32 and 99 leaving remainders of 5 and 8 respectively is **1**.