The HCF of the fractions $\frac{2}{3},\frac{4}{5}$ and $\frac{6}{7}$ is:

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

1. **HCF of Numerators ($2,4,6$):**
The highest common factor dividing $2,4,$ and $6$ is $2$.
2. **LCM of Denominators ($3,5,7$):**
Since $3,5,$ and $7$ are all co-prime numbers, their Least Common Multiple (LCM) is their product:

$$\text{LCM}=3\times 5\times 7=105$$

Combining these values yields:

$$\text{HCF}=\frac{2}{105}$$