Find the HCF of 224, 252 and 84 by long division method

Answer

To find the HCF (Highest Common Factor) of 224, 252, and 84 using the long division method, we will follow these steps:

### Step 1: Start with the two largest numbers
We will begin by finding the HCF of the two largest numbers, which are 224 and 252.

### Step 2: Divide the larger number by the smaller number
We divide 252 by 224.

- **Calculation**:
- 252 ÷ 224 = 1 (remainder 28)
- This means 252 = 224 × 1 + 28

### Step 3: Now, take the remainder and divide the previous divisor
Next, we take the remainder (28) and divide it into the previous divisor (224).

- **Calculation**:
- 224 ÷ 28 = 8 (remainder 0)
- This means 224 = 28 × 8 + 0

Since the remainder is now 0, we conclude that the HCF of 224 and 252 is 28.

### Step 4: Now, find the HCF of the result with the third number
Next, we need to find the HCF of 28 (the result from the previous step) and the third number, which is 84.

- **Calculation**:
- 84 ÷ 28 = 3 (remainder 0)
- This means 84 = 28 × 3 + 0

Since the remainder is 0 again, we conclude that the HCF of 28 and 84 is also 28.

### Conclusion
Thus, the HCF of 224, 252, and 84 is **28**.

---