What is the Highest Common Factor (HCF) of $234$ and $452$?

Let's find the Highest Common Factor (HCF) using the prime factorization method:
1. Prime factorization of $234$:

$$234=2\times 117=2\times 3\times 39=2\times 3^2\times 13$$

2. Prime factorization of $452$:

$$452=2\times 226=2\times 2\times 113=2^2\times 113$$

(Note: $113$ is a prime number)
3. Identify the common prime factors with the lowest power:
The only common prime factor is $2$, and its lowest power present in both configurations is $2^1$.

Therefore, $\text{HCF}(234,452)=2$.