1. **State the problem:** Reduce the fraction $\frac{4}{64}$ to its simplest form. 2. **Formula and rules:** To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD). 3. **Find the GCD:** The factors of 4 are 1, 2, 4. The factors of 64 are 1, 2, 4, 8, 16, 32, 64. The greatest common divisor is 4. 4. **Divide numerator and denominator by the GCD:** $$\frac{4}{64} = \frac{\cancel{4}^1}{\cancel{64}^{16}} = \frac{1}{16}$$ 5. **Final answer:** The fraction $\frac{4}{64}$ simplified is $\frac{1}{16}$.