Problem:
Let be the greatest five-digit number whose digits have a product of . What is the sum of the digits of
Answer Choices:
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Solution:
The leftmost digit of must be the greatest single-digit factor of . Note that is a factor of , but is not, hence the leftmost digit of N must be . Because cannot be a digit, it follows that must be immediately to the right of the , and must be immediately to the right of the . The remaining rightmost two digits of N must be , so that . Thus the sum of the digits of is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions