Smallest number with digit product 10000

What is the smallest positive integer whose digits multiply together to give $10000$ ?

Show hints (2)+

$10000=2^4\cdot5^4$ . The four $5$ s must be four digit- $5$ s; the $2^4$ needs at least two digits ( $8\cdot2$ or $4\cdot4$ ).
Six digits minimum - pick the set with the smallest ascending arrangement.

Answer

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255558

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