Find the HCF of 12.05 and 13.5.

Options

A. `0.25`
B. `0.5`
C. `0.05`
D. `0.005`

Answer

To find the HCF (Highest Common Factor) of 12.05 and 13.5, we can follow these steps:

### Step 1: Remove the Decimal Points
To simplify the calculation, we first convert the decimal numbers into whole numbers. We can do this by multiplying both numbers by 100 (since the highest number of decimal places is 2).

- \( 12.05 \times 100 = 1205 \)
- \( 13.5 \times 100 = 1350 \)

### Step 2: Factor the Whole Numbers
Next, we need to find the prime factors of both 1205 and 1350.

**Factoring 1205:**
- Divide by 5: \( 1205 \div 5 = 241 \)
- 241 is a prime number.

So, the prime factorization of 1205 is:
\[ 1205 = 5 \times 241 \]

**Factoring 1350:**
- Divide by 5: \( 1350 \div 5 = 270 \)
- Divide by 5 again: \( 270 \div 5 = 54 \)
- Divide by 2: \( 54 \div 2 = 27 \)
- Divide by 3: \( 27 \div 3 = 9 \)
- Divide by 3 again: \( 9 \div 3 = 3 \)
- Divide by 3 again: \( 3 \div 3 = 1 \)

So, the prime factorization of 1350 is:
\[ 1350 = 5^2 \times 2 \times 3^3 \]

### Step 3: Identify Common Factors
Now we will identify the common prime factors from both numbers:
- The common factor is \( 5 \).

### Step 4: Calculate the HCF
The HCF is the product of the lowest powers of the common prime factors:
- Here, the only common factor is \( 5 \).

### Step 5: Adjust for the Decimal
Since we multiplied both numbers by 100 to remove the decimals, we need to divide the HCF by 100 to get the actual HCF of the original numbers:
\[ \text{HCF} = \frac{5}{100} = 0.05 \]

### Final Answer
The HCF of 12.05 and 13.5 is:
\[ \text{HCF} = 0.05 \]

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