Find the HCF of 513 and 783.

Answer

To find the HCF (Highest Common Factor) of 513 and 783, we can use the prime factorization method or the division method. Here, I will demonstrate the division method.

### Step-by-Step Solution:

**Step 1: Divide the larger number by the smaller number.**
- We start with the two numbers: 783 and 513.
- Divide 783 by 513.

\[ 783 \div 513 = 1 \quad \text{(remainder: } 783 - 513 = 270\text{)} \]

**Step 2: Replace the larger number with the smaller number and the smaller number with the remainder.**
- Now, we take 513 and 270.

\[ 513 \div 270 = 1 \quad \text{(remainder: } 513 - 270 = 243\text{)} \]

**Step 3: Repeat the process.**
- Next, we take 270 and 243.

\[ 270 \div 243 = 1 \quad \text{(remainder: } 270 - 243 = 27\text{)} \]

**Step 4: Continue until the remainder is 0.**
- Now, we take 243 and 27.

\[ 243 \div 27 = 9 \quad \text{(remainder: } 243 - (27 \times 9) = 0\text{)} \]

**Step 5: Identify the last non-zero remainder.**
- The last non-zero remainder is 27.

Thus, the HCF of 513 and 783 is **27**.