Find the HCF of $2^2\times 3^5\times 5^3$ and $2^4\times 3^2\times 5^1$.

To find the Highest Common Factor (HCF) of numbers expressed as a product of prime factors, we take the minimum power of each common prime factor appearing in both expressions.
Given expressions:

* Expression 1: $2^2\times 3^5\times 5^3$
* Expression 2: $2^4\times 3^2\times 5^1$

Comparing powers of prime bases:

* For base 2: $\min (2,4)=2⟹2^2$
* For base 3: $\min (5,2)=2⟹3^2$
* For base 5: $\min (3,1)=1⟹5^1=5$

Multiplying these together gives the HCF:

$$\text{HCF}=2^2\times 3^2\times 5$$