The H.C.F of 0.54 ,1.8 and 7.2

Options

A. 1.8
B. 0.18
C. 0.018
D. 18

Answer

To find the H.C.F (Highest Common Factor) of the numbers 0.54, 1.8, and 7.2, we will follow these steps:

### Step 1: Convert the decimal numbers to fractions.
- 0.54 can be written as \( \frac{54}{100} \).
- 1.8 can be written as \( \frac{18}{10} \).
- 7.2 can be written as \( \frac{72}{10} \).

### Step 2: Simplify the fractions.
- \( \frac{54}{100} \) simplifies to \( \frac{27}{50} \) (by dividing both numerator and denominator by 2).
- \( \frac{18}{10} \) simplifies to \( \frac{9}{5} \) (by dividing both numerator and denominator by 2).
- \( \frac{72}{10} \) simplifies to \( \frac{36}{5} \) (by dividing both numerator and denominator by 2).

### Step 3: Find the H.C.F of the numerators.
Now we have the simplified fractions:
- \( \frac{27}{50} \)
- \( \frac{9}{5} \)
- \( \frac{36}{5} \)

We will find the H.C.F of the numerators: 27, 9, and 36.

- The factors of 27 are: 1, 3, 9, 27
- The factors of 9 are: 1, 3, 9
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are: 1, 3, 9. The highest common factor is 9.

### Step 4: Find the L.C.M of the denominators.
Next, we find the L.C.M of the denominators: 50, 5, and 5.

- The factors of 50 are: 1, 2, 5, 10, 25, 50
- The factors of 5 are: 1, 5

The L.C.M of 50 and 5 is 50.

### Step 5: Write the H.C.F in fractional form.
Now we can express the H.C.F of the original decimal numbers as:
\[ \text{H.C.F} = \frac{\text{H.C.F of numerators}}{\text{L.C.M of denominators}} = \frac{9}{50} \]

### Step 6: Convert the fraction back to decimal.
To convert \( \frac{9}{50} \) back to decimal:
\[ \frac{9}{50} = 0.18 \]

### Final Answer:
The H.C.F of 0.54, 1.8, and 7.2 is **0.18**.

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