Find the HCF of $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}$.

The formula to find the Highest Common Factor (HCF) of a set of fractions is:
$$\text{HCF of Fractions}=\frac{\text{HCF of Numerators}}{\text{LCM of Denominators}}$$

The given fractions are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}$.

1. **Find HCF of Numerators ($1,2,3,4$):**
Since the number $1$ has no common factors with others besides $1$:

$$\text{HCF}(1,2,3,4)=1$$

2. **Find LCM of Denominators ($2,3,4,5$):**
* Prime factorization: $2=2^1$, $3=3^1$, $4=2^2$, $5=5^1$
* $\text{LCM}=2^2\times 3^1\times 5^1=4\times 3\times 5=60$

Substituting these back into the formula:

$$\text{HCF}=\frac{1}{60}$$