Problem 18 · 2025 Math Kangaroo
Medium
Number Theory
factorizationdigit-sum
The number N is the largest 6-digit number for which the product of all its digits is 180. What is the sum of the digits of the number N?
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Answer: A — 21
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Hint 1 of 2
180 = 2²·3²·5; you need six digits whose product is 180.
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Hint 2 of 2
To make N largest, put the biggest digits first and pad with 1s.
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Approach: greedy largest digits, pad with ones
- Factor 180 into single digits, using as few non-1 digits as possible with large values: 9, 5, 4 (9×5×4 = 180).
- Pad to six digits with three 1s and order descending: 954111.
- Digit sum = 9+5+4+1+1+1 = 21.
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