Find the HCF of 288 and 1080 by the division method.

Answer

To find the HCF (Highest Common Factor) of 288 and 1080 using the division method, we will follow these steps:

### Step 1: Divide the larger number by the smaller number.
We start by dividing 1080 by 288.

\[ 1080 \div 288 \]

### Step 2: Calculate the quotient and remainder.
Now, we calculate how many times 288 fits into 1080.

\[ 288 \times 3 = 864 \]

Now subtract 864 from 1080 to find the remainder.

\[ 1080 - 864 = 216 \]

So, we have:

\[ 1080 = 288 \times 3 + 216 \]

### Step 3: Repeat the process with the smaller number and the remainder.
Next, we take the previous divisor (288) and divide it by the remainder (216).

\[ 288 \div 216 \]

### Step 4: Calculate the quotient and remainder again.
Now, we calculate how many times 216 fits into 288.

\[ 216 \times 1 = 216 \]

Now subtract 216 from 288 to find the new remainder.

\[ 288 - 216 = 72 \]

So, we have:

\[ 288 = 216 \times 1 + 72 \]

### Step 5: Repeat the process again.
Now, we take the last divisor (216) and divide it by the new remainder (72).

\[ 216 \div 72 \]

### Step 6: Calculate the quotient and remainder one last time.
Now, we calculate how many times 72 fits into 216.

\[ 72 \times 3 = 216 \]

Now subtract 216 from 216 to find the remainder.

\[ 216 - 216 = 0 \]

So, we have:

\[ 216 = 72 \times 3 + 0 \]

### Step 7: Conclusion
Since we have reached a remainder of 0, the last non-zero remainder is the HCF. Therefore, the HCF of 288 and 1080 is:

\[ \text{HCF} = 72 \]