What Is A Heegner Number?

Logic Level 2

000÷0 \large \boxed{\phantom0} \: \boxed{\phantom0} \: \boxed{\phantom0} \div \boxed{\phantom0}

All the digits 6,7,86,7,8 and 99 are used exactly once to fill in the boxes above to form a ratio of a 3-digit integer and a 1-digit integer. If this ratio is an integer, what is the maximum possible value of this ratio?

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