1. The problem is to simplify the fraction $\frac{600}{800}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD). 3. Find the GCD of 600 and 800. 4. The prime factorization of 600 is $2^3 \times 3 \times 5^2$. 5. The prime factorization of 800 is $2^5 \times 5^2$. 6. The common prime factors are $2^3$ and $5^2$, so the GCD is $2^3 \times 5^2 = 8 \times 25 = 200$. 7. Divide numerator and denominator by 200: $$\frac{600 \div 200}{800 \div 200} = \frac{3}{4}$$ 8. Therefore, the simplified form of $\frac{600}{800}$ is $\frac{3}{4}$.