HCF of 2.4, 0.36 and 7.2 is

Options

A. 12
B. 0.12
C. 120
D. 1.2

Answer

To find the HCF (Highest Common Factor) of the numbers 2.4, 0.36, and 7.2, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Decimal to Fraction**:
- Convert each decimal number into a fraction:
- \( 2.4 = \frac{24}{10} \)
- \( 0.36 = \frac{36}{100} \)
- \( 7.2 = \frac{72}{10} \)

2. **Simplify the Fractions**:
- Simplify each fraction to its lowest terms:
- \( \frac{24}{10} = \frac{12}{5} \)
- \( \frac{36}{100} = \frac{9}{25} \)
- \( \frac{72}{10} = \frac{36}{5} \)

3. **Find HCF of the Numerators**:
- The numerators are 12, 9, and 36. We need to find the HCF of these numbers.
- The factors of 12: 1, 2, 3, 4, 6, 12
- The factors of 9: 1, 3, 9
- The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- The common factors are 1 and 3, so the HCF is 3.

4. **Find LCM of the Denominators**:
- The denominators are 5, 25, and 5. We need to find the LCM of these numbers.
- The multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, ...
- The multiples of 25: 25, 50, 75, 100, ...
- The LCM is 25.

5. **Calculate HCF of the Original Numbers**:
- The HCF of the original numbers can be calculated using the formula:
\[ \text{HCF} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{3}{25} \]

6. **Convert to Decimal**:
- Convert \( \frac{3}{25} \) to decimal:
\[ \frac{3}{25} = 0.12 \]

### Final Answer:
The HCF of 2.4, 0.36, and 7.2 is **0.12**.

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