Find the HCF of the numbers in each of the following, using the division method :
58, 70

Answer

To find the HCF (Highest Common Factor) of the numbers 58 and 70 using the division method, we can follow these steps:

### Step 1: Identify the two numbers
We need to find the HCF of 58 and 70.

### Step 2: Set up the division
We will divide the larger number (70) by the smaller number (58).
- Dividend = 70
- Divisor = 58

### Step 3: Perform the division
Now, we divide 70 by 58.
- 70 ÷ 58 = 1 (quotient) with a remainder of 12.

### Step 4: Write the equation
This can be written as:
\[ 70 = 58 \times 1 + 12 \]

### Step 5: Repeat the process
Now, we take the previous divisor (58) and the remainder (12) and repeat the process.
- New Dividend = 58
- New Divisor = 12

Now, we divide 58 by 12.
- 58 ÷ 12 = 4 (quotient) with a remainder of 10.

### Step 6: Write the new equation
This can be written as:
\[ 58 = 12 \times 4 + 10 \]

### Step 7: Repeat again
Now, we take the previous divisor (12) and the remainder (10).
- New Dividend = 12
- New Divisor = 10

Now, we divide 12 by 10.
- 12 ÷ 10 = 1 (quotient) with a remainder of 2.

### Step 8: Write the new equation
This can be written as:
\[ 12 = 10 \times 1 + 2 \]

### Step 9: Continue the process
Now, we take the previous divisor (10) and the remainder (2).
- New Dividend = 10
- New Divisor = 2

Now, we divide 10 by 2.
- 10 ÷ 2 = 5 (quotient) with a remainder of 0.

### Step 10: Write the final equation
This can be written as:
\[ 10 = 2 \times 5 + 0 \]

### Step 11: Conclusion
Since we have reached a remainder of 0, the last divisor (2) is the HCF of 58 and 70.

Thus, the HCF of 58 and 70 is **2**.

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