H.C.F of `1/2, 2/3, 3/4, 4/5` is -

Options

A. 1
B. 12
C. `4/5`
D. `1/(60)`

Answer

To find the H.C.F. (Highest Common Factor) of the fractions \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5} \), we can use the following formula:

\[ \text{H.C.F. of } \frac{a}{b} = \frac{\text{H.C.F. of } a}{\text{L.C.M. of } b} \]

### Step-by-Step Solution:

1. **Identify the Numerators and Denominators:**
- The numerators are: \( 1, 2, 3, 4 \)
- The denominators are: \( 2, 3, 4, 5 \)

2. **Find the H.C.F. of the Numerators:**
- The numerators are \( 1, 2, 3, 4 \).
- The H.C.F. of \( 1, 2, 3, 4 \) is \( 1 \) (since 1 is the only common factor).

3. **Find the L.C.M. of the Denominators:**
- The denominators are \( 2, 3, 4, 5 \).
- The L.C.M. of \( 2, 3, 4, 5 \):
- The prime factorization is:
- \( 2 = 2^1 \)
- \( 3 = 3^1 \)
- \( 4 = 2^2 \)
- \( 5 = 5^1 \)
- The L.C.M. takes the highest power of each prime:
- \( 2^2, 3^1, 5^1 \)
- Thus, L.C.M. = \( 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \)

4. **Apply the H.C.F. and L.C.M. in the Formula:**
- Now, using the formula:
\[ \text{H.C.F.} = \frac{\text{H.C.F. of numerators}}{\text{L.C.M. of denominators}} = \frac{1}{60} \]

### Final Answer:
The H.C.F. of \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5} \) is \( \frac{1}{60} \).