Problem 17 · 2025 Math Kangaroo
Medium
Number Theory
factorizationfactor-pairs
There are some cards on a table with various different positive integers written on them. All of these are smaller than 20 and their product is 2025. What is the maximum number of cards on the table?
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Answer: D — 5
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Hint 1 of 2
Factor 2025 and split it into as many factors below 20 as possible.
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Hint 2 of 2
2025 = 3^4 × 5^2; including the card '1' adds one more card for free.
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Approach: maximize the number of small factors
- 2025 = 3⁴ × 5²; each card value is below 20.
- Break it up as 1 × 3 × 5 × 9 × 15 = 2025, all distinct and under 20.
- That gives 5 cards.
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