What is the HCF of 150, 225 and 375?

To find the Highest Common Factor (HCF) of $150$, $225$, and $375$, use the prime factorization method:
1. Express each number as a product of prime factors:

$$150=2\times 3\times 5^2$$

$$225=3^2\times 5^2$$

$$375=3\times 5^3$$

2. Identify the common prime factors and take the lowest power of each:
* The prime factor $2$ is not common to all numbers.
* The prime factor $3$ is common, and its lowest power is $3^1$.
* The prime factor $5$ is common, and its lowest power is $5^2$.

3. Multiply these lowest powers together to find the HCF:

$$\text{HCF}=3^1\times 5^2=3\times 25=75$$

Hence, the HCF is $75$.