1. **State the problem:** Find the highest power of 20 that divides 50!. 2. **Prime factorize 20:** $$20 = 2^2 \times 5$$ 3. **Find the exponent of 2 in 50!:** Use Legendre's formula: $$\left\lfloor \frac{50}{2} \right\rfloor + \left\lfloor \frac{50}{4} \right\rfloor + \left\lfloor \frac{50}{8} \right\rfloor + \left\lfloor \frac{50}{16} \right\rfloor + \left\lfloor \frac{50}{32} \right\rfloor = 25 + 12 + 6 + 3 + 1 = 47$$ 4. **Find the exponent of 5 in 50!:** $$\left\lfloor \frac{50}{5} \right\rfloor + \left\lfloor \frac{50}{25} \right\rfloor = 10 + 2 = 12$$ 5. **Determine the highest power of 20 dividing 50!:** Since $$20 = 2^2 \times 5$$, the power of 20 dividing 50! is limited by the smaller of $$\left\lfloor \frac{47}{2} \right\rfloor = 23$$ and $$12$$. 6. **Final answer:** The highest power of 20 dividing 50! is $$12$$.