Find the HCF of `1/2 , 3/4 and 4/5`

Options

A. `1/(20)`
B. `1/(40)`
C. 20
D. 15

Answer

To find the HCF (Highest Common Factor) of the fractions \( \frac{1}{2}, \frac{3}{4}, \) and \( \frac{4}{5} \), we can follow these steps:

### Step 1: Identify the Numerators and Denominators
The fractions given are:
- Numerators: \( 1, 3, 4 \)
- Denominators: \( 2, 4, 5 \)

### Step 2: Find the HCF of the Numerators
Now, we need to find the HCF of the numerators \( 1, 3, \) and \( 4 \).
- The factors of \( 1 \) are \( 1 \).
- The factors of \( 3 \) are \( 1, 3 \).
- The factors of \( 4 \) are \( 1, 2, 4 \).

The only common factor among \( 1, 3, \) and \( 4 \) is \( 1 \).
Thus, \( \text{HCF of } (1, 3, 4) = 1 \).

### Step 3: Find the HCF of the Denominators
Next, we find the HCF of the denominators \( 2, 4, \) and \( 5 \).
- The factors of \( 2 \) are \( 1, 2 \).
- The factors of \( 4 \) are \( 1, 2, 4 \).
- The factors of \( 5 \) are \( 1, 5 \).

The only common factor among \( 2, 4, \) and \( 5 \) is \( 1 \) and \( 2 \).
Thus, \( \text{HCF of } (2, 4, 5) = 2 \).

### Step 4: Calculate the HCF of the Fractions
Now we can find the HCF of the fractions using the formula:
\[ \text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{HCF of denominators}} = \frac{1}{2} \]

### Step 5: Final Result
Thus, the HCF of \( \frac{1}{2}, \frac{3}{4}, \) and \( \frac{4}{5} \) is:
\[ \frac{1}{2} \]

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