Problem 1473
The multiplicative digital root of a number is the single digit obtained by repeatedly multiplying its digits until a single-digit number is reached. The process stops when the result is a number less than 10. For example, the multiplicative digital root if 376 is found by 3 x 7 x 6 = 126 then 1 x 2 x 6 = 12 then 1 x 2 = 2. Find the largest 4-digit number with a multiplicative digital root of 2.
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