Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

Answer

To find the greatest number that divides 285 and 1249 leaving remainders 9 and 7 respectively, we can follow these steps:

### Step 1: Adjust the numbers by subtracting the remainders
To find the actual numbers that we need to work with, we will subtract the remainders from the original numbers.

- For 285, subtract 9:
\[ 285 - 9 = 276 \]

- For 1249, subtract 7:
\[ 1249 - 7 = 1242 \]

### Step 2: Find the Highest Common Factor (HCF) of the adjusted numbers
Now, we need to find the HCF of 276 and 1242. We can do this using the division method.

1. **Divide 1242 by 276**:
- 1242 ÷ 276 = 4 (since 4 × 276 = 1104)
- Remainder = 1242 - 1104 = 138

2. **Now, divide 276 by the remainder 138**:
- 276 ÷ 138 = 2 (since 2 × 138 = 276)
- Remainder = 276 - 276 = 0

### Step 3: Conclusion
Since the remainder is now 0, the last non-zero remainder is the HCF. Thus, the HCF of 276 and 1242 is 138.

Therefore, the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is **138**.

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