Find the HCF of each of the following by common division method.
216, 315, 180

Answer

To find the HCF (Highest Common Factor) of the numbers 216, 315, and 180 using the common division method, we will follow these steps:

### Step 1: Arrange the Numbers
We have three numbers: 216, 315, and 180. We will arrange them in descending order for convenience.
- 315
- 216
- 180

### Step 2: Divide the Largest Number by the Next Largest
We start by dividing the largest number (315) by the next largest number (216).

\[ 315 \div 216 = 1 \quad \text{(remainder = 315 - 216 = 99)} \]

### Step 3: Continue with the Remainder
Now, we take the remainder (99) and divide it into the previous divisor (216).

\[ 216 \div 99 = 2 \quad \text{(remainder = 216 - 2 \times 99 = 18)} \]

### Step 4: Repeat the Process
Next, we take the remainder (18) and divide it into the previous divisor (99).

\[ 99 \div 18 = 5 \quad \text{(remainder = 99 - 5 \times 18 = 9)} \]

### Step 5: Continue Again
Now, we take the remainder (9) and divide it into the previous divisor (18).

\[ 18 \div 9 = 2 \quad \text{(remainder = 18 - 2 \times 9 = 0)} \]

### Step 6: Conclusion
Since we have reached a remainder of 0, the last non-zero remainder is the HCF. Therefore, the HCF of 216, 315, and 180 is:

**HCF = 9**