Problem 14 · 2014 Math Kangaroo
Medium
Number Theory
factorizationdigit-sum
When the three digits of a three-digit number are multiplied together, the product is 135. What do you get when you add the three digits?
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Answer: D — 17
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Hint 1 of 2
Break 135 into a product of three single digits.
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Hint 2 of 2
Factor 135 = 27 × 5 = 3 × 9 × 5; those are the only single-digit factors that work.
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Approach: factor 135 into three single digits, then add
- 135 = 27 × 5 = 3 × 9 × 5, and 3, 9, 5 are all single digits.
- No other split of 135 gives three single-digit factors.
- Adding them: 3 + 9 + 5 = 17.
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