The HCF of is 4/15, 6/25and16/25

Options

A. `(2)/(75)`
B. `(16)/(5)`
C. `(6)/(25)`
D. None of these

Answer

To find the HCF (Highest Common Factor) of the fractions \( \frac{4}{15}, \frac{6}{25}, \frac{16}{25} \), we follow these steps:

### Step 1: Identify the Numerators and Denominators
We will first separate the numerators and denominators of the given fractions:
- Numerators: 4, 6, 16
- Denominators: 15, 25, 25

### Step 2: Find the HCF of the Numerators
Next, we need to find the HCF of the numerators (4, 6, and 16).
- The factors of 4 are: 1, 2, 4
- The factors of 6 are: 1, 2, 3, 6
- The factors of 16 are: 1, 2, 4, 8, 16

The common factors are: 1, 2. The highest of these is 2.
Thus, HCF of the numerators = 2.

### Step 3: Find the LCM of the Denominators
Now, we will find the LCM of the denominators (15, 25, and 25).
- The prime factorization of 15 is \( 3 \times 5 \).
- The prime factorization of 25 is \( 5^2 \).

To find the LCM, we take the highest power of each prime:
- For 3: \( 3^1 \)
- For 5: \( 5^2 \)

Thus, LCM = \( 3^1 \times 5^2 = 3 \times 25 = 75 \).

### Step 4: Form the HCF of the Fractions
Now that we have the HCF of the numerators and the LCM of the denominators, we can form the HCF of the fractions:
\[ \text{HCF} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{2}{75} \]

### Final Answer
The HCF of the fractions \( \frac{4}{15}, \frac{6}{25}, \frac{16}{25} \) is \( \frac{2}{75} \).

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