Find the HCF of the following numbers using division method
224, 210, 280

Answer

To find the HCF (Highest Common Factor) of the numbers 224, 210, and 280 using the division method, we can follow these steps:

### Step 1: Divide the two largest numbers
We will start by dividing the two largest numbers, which are 280 and 210.

- **Calculation**:
\[ 280 \div 210 = 1 \quad \text{(remainder = 280 - 210 = 70)} \]
So, we have:
- Quotient = 1
- Remainder = 70

### Step 2: Divide the previous divisor by the remainder
Next, we will take the divisor (210) and divide it by the remainder (70).

- **Calculation**:
\[ 210 \div 70 = 3 \quad \text{(remainder = 210 - 70 \times 3 = 0)} \]
So, we have:
- Quotient = 3
- Remainder = 0

Since the remainder is now 0, we can conclude that the HCF of 210 and 280 is 70.

### Step 3: Divide the HCF by the next number
Now, we will take the HCF (70) and divide it by the next number, which is 224.

- **Calculation**:
\[ 224 \div 70 = 3 \quad \text{(remainder = 224 - 70 \times 3 = 14)} \]
So, we have:
- Quotient = 3
- Remainder = 14

### Step 4: Divide the previous divisor by the remainder
Next, we will take the divisor (70) and divide it by the remainder (14).

- **Calculation**:
\[ 70 \div 14 = 5 \quad \text{(remainder = 70 - 14 \times 5 = 0)} \]
So, we have:
- Quotient = 5
- Remainder = 0

### Conclusion
Since the remainder is now 0, we can conclude that the HCF of 224, 210, and 280 is 14.

Thus, the HCF of 224, 210, and 280 is **14**.

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