Find the HCF of 72, 108 and 126 using division

Options

A. `18`
B. `22`
C. `16`
D. `20`

Answer

To find the HCF (Highest Common Factor) of 72, 108, and 126 using the division method, we can follow these steps:

### Step 1: Find HCF of 72 and 108
1. **Divide 108 by 72**:
- 108 ÷ 72 = 1 (quotient) with a remainder of 36.
- Calculation: 108 - (72 × 1) = 108 - 72 = 36.

2. **Now, divide 72 by the remainder (36)**:
- 72 ÷ 36 = 2 (quotient) with a remainder of 0.
- Calculation: 72 - (36 × 2) = 72 - 72 = 0.

Since the remainder is now 0, the HCF of 72 and 108 is 36.

### Step 2: Find HCF of the result (36) and the third number (126)
1. **Divide 126 by 36**:
- 126 ÷ 36 = 3 (quotient) with a remainder of 18.
- Calculation: 126 - (36 × 3) = 126 - 108 = 18.

2. **Now, divide 36 by the remainder (18)**:
- 36 ÷ 18 = 2 (quotient) with a remainder of 0.
- Calculation: 36 - (18 × 2) = 36 - 36 = 0.

Since the remainder is now 0, the HCF of 36 and 126 is 18.

### Conclusion
Thus, the HCF of 72, 108, and 126 is **18**.

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