Fnd the HCF of 867 and 255

Answer

To find the HCF (Highest Common Factor) of 867 and 255 using the long division method, follow these steps:

### Step 1: Divide the larger number by the smaller number
We start by dividing 867 by 255.

\[ 867 \div 255 = 3 \quad \text{(since } 255 \times 3 = 765\text{)} \]

### Step 2: Calculate the remainder
Now, we subtract the product from the larger number to find the remainder.

\[ 867 - 765 = 102 \]

### Step 3: Replace the larger number with the smaller number
Now, we replace 867 with 255 and 255 with the remainder 102. We will now divide 255 by 102.

\[ 255 \div 102 = 2 \quad \text{(since } 102 \times 2 = 204\text{)} \]

### Step 4: Calculate the new remainder
Subtract the product from 255 to find the new remainder.

\[ 255 - 204 = 51 \]

### Step 5: Repeat the process
Now, we replace 255 with 102 and 102 with the new remainder 51. We will now divide 102 by 51.

\[ 102 \div 51 = 2 \quad \text{(since } 51 \times 2 = 102\text{)} \]

### Step 6: Calculate the final remainder
Subtract the product from 102 to find the final remainder.

\[ 102 - 102 = 0 \]

### Step 7: Conclusion
Since the remainder is now 0, the divisor at this step (51) is the HCF of 867 and 255.

\[ \text{HCF} = 51 \]

### Final Answer:
The HCF of 867 and 255 is **51**.

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