The sum of the base-\( 10 \) logarithms of the factors of \( 10^n \) is 792 (\( \log n_1+\log n_2+...\log n_k \)) where \( n_k \) are the factors of \( 10^n \). What is \( n \)?

EDIT: The problem has been updated to \( 10^n \) instead of \( 10n \).

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