1. The problem asks to find the missing prime factor in the factorization of 800 given as $$800 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times \ldots$$ 2. First, calculate the product of the known factors: $$2 \times 2 \times 2 \times 2 \times 2 = 2^5 = 32$$ 3. Multiply this by 5: $$32 \times 5 = 160$$ 4. Since the product of the known factors is 160, the missing factor must satisfy: $$160 \times \text{missing factor} = 800$$ 5. Solve for the missing factor: $$\text{missing factor} = \frac{800}{160} = 5$$ 6. Therefore, the missing prime factor is 5. Final answer: $$5$$