Find the HCF of $0.05,0.5,0.25,1.25$.

1. Convert the given decimals into fractions with a common denominator:
* $0.05=\frac{5}{100}$
* $0.5=\frac{50}{100}$
* $0.25=\frac{25}{100}$
* $1.25=\frac{125}{100}$

2. The formula for the HCF of fractions is:

$$\text{HCF}=\frac{\text{HCF of Numerators}}{\text{LCM of Denominators}}$$

3. Find the HCF of the numerators ($5,50,25,125$):
* Factors of $5=5$
* Factors of $25=5^2$
* Factors of $50=2\times 5^2$
* Factors of $125=5^3$
* $\text{HCF}(5,50,25,125)=5$

4. Find the LCM of the denominators ($100,100,100,100$):
* $\text{LCM}=100$

5. Calculate the overall HCF:

$$\text{HCF}=\frac{5}{100}=0.05$$