Find H.C.F. of 54, 144, 210.

Options

A. `6`
B. `8`
C. `4`
D. `10`

Answer

To find the H.C.F. (Highest Common Factor) of the numbers 54, 144, and 210 using the division method, we can follow these steps:

### Step 1: Find HCF of the first two numbers (54 and 144)
1. **Divide the larger number by the smaller number**:
- Divide 144 by 54.
- 144 ÷ 54 = 2 (remainder 36).
- Calculation: 144 - (54 × 2) = 144 - 108 = 36.

2. **Now, divide the previous divisor (54) by the remainder (36)**:
- 54 ÷ 36 = 1 (remainder 18).
- Calculation: 54 - (36 × 1) = 54 - 36 = 18.

3. **Now, divide the previous divisor (36) by the new remainder (18)**:
- 36 ÷ 18 = 2 (remainder 0).
- Calculation: 36 - (18 × 2) = 36 - 36 = 0.

Since the remainder is now 0, the last non-zero remainder is the HCF of 54 and 144, which is **18**.

### Step 2: Find HCF of the result (18) with the third number (210)
1. **Now, divide 210 by the HCF found (18)**:
- 210 ÷ 18 = 11 (remainder 12).
- Calculation: 210 - (18 × 11) = 210 - 198 = 12.

2. **Now, divide the previous divisor (18) by the remainder (12)**:
- 18 ÷ 12 = 1 (remainder 6).
- Calculation: 18 - (12 × 1) = 18 - 12 = 6.

3. **Now, divide the previous divisor (12) by the new remainder (6)**:
- 12 ÷ 6 = 2 (remainder 0).
- Calculation: 12 - (6 × 2) = 12 - 12 = 0.

Since the remainder is now 0, the last non-zero remainder is the HCF of 18 and 210, which is **6**.

### Conclusion
Thus, the H.C.F. of 54, 144, and 210 is **6**.

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