Find the HCF of 0.9 , 0.36 and 1.08.

Answer

To find the HCF (Highest Common Factor) of the numbers 0.9, 0.36, and 1.08, we can follow these steps:

### Step 1: Convert the decimals to fractions
First, we convert each decimal into a fraction for easier calculation.

- 0.9 = 9/10
- 0.36 = 36/100 = 9/25 (simplified)
- 1.08 = 108/100 = 27/25 (simplified)

### Step 2: Find the HCF of the numerators
Now, we need to find the HCF of the numerators of the fractions we obtained.

- The numerators are 9, 9, and 27.

To find the HCF of 9, 9, and 27:
- The factors of 9 are: 1, 3, 9
- The factors of 27 are: 1, 3, 9, 27

The common factors are 1, 3, and 9. The highest of these is 9.

### Step 3: Find the LCM of the denominators
Next, we find the LCM (Lowest Common Multiple) of the denominators of the fractions.

- The denominators are 10, 25, and 25.

To find the LCM of 10 and 25:
- The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
- The multiples of 25 are: 25, 50, 75, 100, ...

The least common multiple is 50.

### Step 4: Calculate the HCF of the original decimals
Now we can find the HCF of the original decimals by using the formula:
\[ \text{HCF} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} \]

So, we have:
\[ \text{HCF} = \frac{9}{50} \]

### Step 5: Convert back to decimal
Finally, we convert the fraction back to decimal form:
\[ \text{HCF} = 0.18 \]

Thus, the HCF of 0.9, 0.36, and 1.08 is **0.18**.

---