The greatest number. Which when divide 989 and 1327 leave remainders 5 and 7 respectively. is

Options

A. 8
B. 16
C. 24
D. 34

Answer

To solve the problem of finding the greatest number which, when divided by 989 and 1327, leaves remainders of 5 and 7 respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers and Remainders**:
- The first number is 989, and the remainder is 5.
- The second number is 1327, and the remainder is 7.

2. **Subtract the Remainders from the Numbers**:
- For 989:
\[ 989 - 5 = 984 \]
- For 1327:
\[ 1327 - 7 = 1320 \]

3. **Find the HCF (Highest Common Factor)**:
- Now we need to find the HCF of 984 and 1320.
- We can use the prime factorization method or the Euclidean algorithm to find the HCF.

4. **Using the Euclidean Algorithm**:
- Divide 1320 by 984:
\[ 1320 \div 984 \approx 1 \quad (\text{remainder } 336) \]
- Now, take 984 and divide it by the remainder 336:
\[ 984 \div 336 \approx 2 \quad (\text{remainder } 312) \]
- Next, divide 336 by 312:
\[ 336 \div 312 \approx 1 \quad (\text{remainder } 24) \]
- Now, divide 312 by 24:
\[ 312 \div 24 = 13 \quad (\text{remainder } 0) \]
- Since the remainder is now 0, the last non-zero remainder is the HCF.

5. **Conclusion**:
- The HCF of 984 and 1320 is 24.
- Therefore, the greatest number which when divided by 989 and 1327 leaves remainders of 5 and 7 respectively is **24**.