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Answer:
To find the number of equal parts into which 50 should be divided to maximize the continued product, we use the concept that the parts should be as equal as possible. By setting the derivative of the logarithm of the product function to zero, we find that the optimal number of parts is approximately \( \frac{50}{e} \), which is around 18.4. Thus, the best integer values to consider are 18 and 19, and checking these values shows that dividing 50 into 18 or 19 parts yields the maximum continued product.