Find the HCF of `4/5 and 7/(15)`

Options

A. `1/(13)`
B. `1/5`
C. `1/(15)`
D. `(1)/(25)`

Answer

To find the HCF (Highest Common Factor) of the fractions \( \frac{4}{5} \) and \( \frac{7}{15} \), we can follow these steps:

### Step 1: Identify the Numerators and Denominators
The fractions are \( \frac{4}{5} \) and \( \frac{7}{15} \). Here, the numerators are 4 and 7, and the denominators are 5 and 15.

### Step 2: Find the HCF of the Numerators
We need to find the HCF of the numerators 4 and 7.
- The factors of 4 are: 1, 2, 4
- The factors of 7 are: 1, 7

The common factor is 1. Therefore,
\[ \text{HCF of 4 and 7} = 1 \]

### Step 3: Find the HCF of the Denominators
Next, we find the HCF of the denominators 5 and 15.
- The factors of 5 are: 1, 5
- The factors of 15 are: 1, 3, 5, 15

The common factor is 5. Therefore,
\[ \text{HCF of 5 and 15} = 5 \]

### Step 4: Calculate the HCF of the Fractions
Now we can use the formula for the HCF of fractions:
\[ \text{HCF} \left( \frac{a}{b}, \frac{c}{d} \right) = \frac{\text{HCF of numerators}}{\text{HCF of denominators}} \]
Substituting the values we found:
\[ \text{HCF} \left( \frac{4}{5}, \frac{7}{15} \right) = \frac{\text{HCF of 4 and 7}}{\text{HCF of 5 and 15}} = \frac{1}{5} \]

### Final Answer
Thus, the HCF of \( \frac{4}{5} \) and \( \frac{7}{15} \) is \( \frac{1}{5} \).

---