Find the HCF of 84 and 112 by division method.

Explanation

To find the HCF (Highest Common Factor) of 84 and 112 using the division method, follow these steps:

### Step-by-Step Solution:

1. **Identify the two numbers**: We need to find the HCF of 84 and 112.

2. **Set up the division**: Start by dividing the larger number (112) by the smaller number (84).
\[ 112 \div 84 \]

3. **Perform the division**:
- 84 goes into 112 one time.
- Calculate the remainder:
\[ 112 - (84 \times 1) = 112 - 84 = 28 \]

4. **Repeat the process**: Now, take the divisor (84) and divide it by the remainder (28).
\[ 84 \div 28 \]

5. **Perform the second division**:
- 28 goes into 84 three times.
- Calculate the remainder:
\[ 84 - (28 \times 3) = 84 - 84 = 0 \]

6. **Conclusion**: Since the remainder is now 0, the last non-zero remainder is the HCF. Therefore, the HCF of 84 and 112 is:
\[ \text{HCF} = 28 \]

### Final Answer:
The HCF of 84 and 112 is **28**.