Problem 5 · 2009 Math Kangaroo
Medium
Number Theory
factorizationfactor-triples
The product of four different natural numbers is 100. What is the sum of the four numbers?
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Answer: D — 18
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Hint 1 of 2
100 = 2²·5²; you need four DIFFERENT factors whose product is 100.
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Hint 2 of 2
Try to peel off the smallest possible factors first.
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Approach: factor 100 into four distinct positive integers
- Write 100 = 1·2·5·10, four different numbers whose product is 100.
- Any other split repeats a factor (e.g. 1·4·5·5) or has too few numbers.
- Their sum is 1 + 2 + 5 + 10 = 18.
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