Find the HCF of the following numbers using: division method
288 and 420

Answer

To find the HCF (Highest Common Factor) of 288 and 420 using the division method, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers**: We have two numbers, 288 and 420. We will start with the larger number, which is 420.

2. **Divide the Larger Number by the Smaller Number**:
- Divide 420 by 288.
- The quotient is 1 and the remainder is calculated as follows:
\[ 420 - (288 \times 1) = 420 - 288 = 132 \]
- So, we write:
\[ 420 = 288 \times 1 + 132 \]

3. **Repeat the Process**: Now, we take the divisor (288) and divide it by the remainder (132).
- Divide 288 by 132.
- The quotient is 2 and the remainder is:
\[ 288 - (132 \times 2) = 288 - 264 = 24 \]
- So, we write:
\[ 288 = 132 \times 2 + 24 \]

4. **Continue Dividing**: Now, take the last divisor (132) and divide it by the new remainder (24).
- Divide 132 by 24.
- The quotient is 5 and the remainder is:
\[ 132 - (24 \times 5) = 132 - 120 = 12 \]
- So, we write:
\[ 132 = 24 \times 5 + 12 \]

5. **Final Division**: Now, take the last divisor (24) and divide it by the new remainder (12).
- Divide 24 by 12.
- The quotient is 2 and the remainder is:
\[ 24 - (12 \times 2) = 24 - 24 = 0 \]
- So, we write:
\[ 24 = 12 \times 2 + 0 \]

6. **Conclusion**: Since the remainder is now 0, the last non-zero remainder is the HCF. Therefore, the HCF of 288 and 420 is **12**.

### Final Answer:
The HCF of 288 and 420 is **12**.