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Problem 616

AIME late

Number theory Difficulty 5.0 Find the answer

1. Find the largest natural number consisting of distinct digits such that the product of the digits of this number is 2016.

Your answer

Official solution

Answer: 876321.

Solution: Factorize the number 2016. $2016=2^{5} \cdot 3^{2} \cdot 7$ . To make the number as large as possible, it should contain the maximum number of digits. Notice that the number must include the digit 1. Therefore, the number should consist of the digits $1,2,3,6,7,8$ .

Grading Criteria. 20 points for the correct answer. 0 points for any other answer.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.