Find the HCF of 42, 84 and 24 by common division method.

Answer

To find the HCF (Highest Common Factor) of 42, 84, and 24 using the common division method, we can follow these steps:

### Step 1: Arrange the Numbers
First, we arrange the numbers in ascending order. Here, we have:
- 24 < 42 < 84

### Step 2: Start with the Smallest Number
We will start by dividing the largest number (84) by the smallest number (24).

### Step 3: Perform Division
- Divide 84 by 24:
- 84 ÷ 24 = 3 (remainder 12)

So, we write it as:
- 84 = 24 × 3 + 12

### Step 4: Use the Remainder
Now, we take the divisor (24) and the remainder (12) and divide them:
- Divide 24 by 12:
- 24 ÷ 12 = 2 (remainder 0)

So, we write it as:
- 24 = 12 × 2 + 0

### Step 5: Identify the HCF
Since the remainder is now 0, the last non-zero remainder (which is 12) is the HCF of 24 and 84.

### Step 6: Check with the Third Number
Now, we need to check if this HCF (12) divides the third number (42) completely:
- Divide 42 by 12:
- 42 ÷ 12 = 3 (remainder 6)

Since 12 does not divide 42 completely, we need to continue the process.

### Step 7: Repeat with the Last Non-Zero Remainder
Now, we take the last divisor (12) and the remainder (6) and divide them:
- Divide 12 by 6:
- 12 ÷ 6 = 2 (remainder 0)

### Step 8: Final HCF
Since the remainder is now 0, the last non-zero remainder (which is 6) is the HCF of 42, 84, and 24.

### Conclusion
Thus, the HCF of 42, 84, and 24 is **6**.

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