Find the HCF of `96, 108, 132` using division by common factors of all the given numbers

Options

A. `5`
B. `8`
C. `12`
D. `9`

Answer

To find the HCF (Highest Common Factor) of the numbers 96, 108, and 132 using the division method, we will follow these steps:

### Step 1: Find HCF of 96 and 132
1. **Set up the division**: We will divide 132 by 96.
- Dividend = 132
- Divisor = 96
2. **Perform the division**:
- 132 ÷ 96 = 1 (since 96 fits into 132 once)
- Remainder = 132 - (96 × 1) = 132 - 96 = 36

### Step 2: Continue with the remainder
3. **Now, use the remainder (36) as the new divisor** and the previous divisor (96) as the new dividend:
- Dividend = 96
- Divisor = 36
4. **Perform the division**:
- 96 ÷ 36 = 2 (since 36 fits into 96 two times)
- Remainder = 96 - (36 × 2) = 96 - 72 = 24

### Step 3: Repeat the process
5. **Now, use the remainder (24) as the new divisor** and the previous divisor (36) as the new dividend:
- Dividend = 36
- Divisor = 24
6. **Perform the division**:
- 36 ÷ 24 = 1 (since 24 fits into 36 once)
- Remainder = 36 - (24 × 1) = 36 - 24 = 12

### Step 4: Continue until the remainder is 0
7. **Now, use the remainder (12) as the new divisor** and the previous divisor (24) as the new dividend:
- Dividend = 24
- Divisor = 12
8. **Perform the division**:
- 24 ÷ 12 = 2 (since 12 fits into 24 two times)
- Remainder = 24 - (12 × 2) = 24 - 24 = 0

### Step 5: HCF of 96 and 132
9. Since the remainder is now 0, the last divisor (12) is the HCF of 96 and 132.

### Step 6: Find HCF of 12 and 108
10. Now we will find the HCF of 12 and 108.
11. **Set up the division**:
- Dividend = 108
- Divisor = 12
12. **Perform the division**:
- 108 ÷ 12 = 9 (since 12 fits into 108 nine times)
- Remainder = 108 - (12 × 9) = 108 - 108 = 0

### Conclusion
13. Since the remainder is 0, the last divisor (12) is the HCF of 12 and 108.

Thus, the HCF of 96, 108, and 132 is **12**.

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