A number theory problem by Pi Han Goh

\[ \large 2^{200} \times 5^{500} = 49\ldots \ldots 5\underbrace{0000000\ldots 0}_{\text{all 0's}} \]

The last \(n\) digits of the product \(2^{200} \times 5^{500} \) consists of all 0's. What is the maximum value of \(n\)?

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