# 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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