1. **State the problem:** Simplify the fraction $\frac{25}{64}$. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). 3. **Find the GCD:** The factors of 25 are 1, 5, 25. The factors of 64 are 1, 2, 4, 8, 16, 32, 64. The greatest common factor is 1. 4. **Simplify the fraction:** Since the GCD is 1, the fraction $\frac{25}{64}$ is already in simplest form. 5. **Final answer:** $\frac{25}{64}$ is the simplified fraction.